A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions

Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered...

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Vydáno v:	Advances in computational mathematics Ročník 50; číslo 1; s. 3
Hlavní autoři:	Zheng, Bo, Shang, Yueqiang
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.02.2024 Springer Nature B.V
Témata:	Algorithms Boundary conditions Computational Mathematics and Numerical Analysis Computational Science and Engineering Defects Fluid flow High Reynolds number Incompressible flow Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Multiscale analysis Reynolds number Stability analysis Stiffness matrix Visualization Defect-correction method Two-grid method Variational multiscale method Stabilized finite element method 76D05 65N55 65N30 Navier-Stokes equations
ISSN:	1019-7168, 1572-9044
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Abstract	Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered and high Reynolds numbers are allowed. In this developed algorithm, we first solve an artificial viscosity stabilized nonlinear problem on a coarse grid in a defect step and then correct the resulting residual by solving two stabilized and linearized problems on a fine grid in correction steps. While the fine grid correction problems have the same stiffness matrices with only different right-hand sides. We use a variational multiscale method to stabilize the system, making the algorithm has a broad range of potential applications in the simulation of high Reynolds number flows. Under the weak uniqueness condition, we give a stability analysis of the present algorithm, analyze the error bounds of the approximate solutions, and derive the algorithmic parameter scalings. Finally, we perform a series of numerical examples to demonstrate the promise of the proposed algorithm.
AbstractList	Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-homogeneous Dirichlet boundary conditions are considered and high Reynolds numbers are allowed. In this developed algorithm, we first solve an artificial viscosity stabilized nonlinear problem on a coarse grid in a defect step and then correct the resulting residual by solving two stabilized and linearized problems on a fine grid in correction steps. While the fine grid correction problems have the same stiffness matrices with only different right-hand sides. We use a variational multiscale method to stabilize the system, making the algorithm has a broad range of potential applications in the simulation of high Reynolds number flows. Under the weak uniqueness condition, we give a stability analysis of the present algorithm, analyze the error bounds of the approximate solutions, and derive the algorithmic parameter scalings. Finally, we perform a series of numerical examples to demonstrate the promise of the proposed algorithm.
ArticleNumber	3
Author	Zheng, Bo Shang, Yueqiang
Author_xml	– sequence: 1 givenname: Bo surname: Zheng fullname: Zheng, Bo organization: School of Mathematics and Statistics, Southwest University – sequence: 2 givenname: Yueqiang surname: Shang fullname: Shang, Yueqiang email: yqshang@swu.edu.cn, shangyueqiang@sina.com organization: School of Mathematics and Statistics, Southwest University
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Cites_doi	10.1137/S0036142992232949 10.1007/s10915-013-9806-9 10.1002/num.22080 10.1002/mma.5365 10.1137/0915016 10.1002/num.20329 10.1007/s10915-017-0593-6 10.1063/1.1332391 10.1016/j.apm.2012.02.051 10.1016/j.cam.2007.02.015 10.1137/S003614299630230X 10.1016/j.camwa.2015.11.011 10.1016/j.apm.2014.04.049 10.1016/j.finel.2011.06.001 10.1016/0045-7825(82)90071-8 10.1002/mma.4608 10.1007/978-3-642-61623-5 10.1016/j.apnum.2012.03.006 10.1016/0045-7825(93)90126-I 10.1137/S1064827596306045 10.1016/j.jcp.2010.05.038 10.1016/j.apnum.2020.09.001 10.1016/j.jmaa.2018.10.002 10.1137/0916014 10.1016/j.jcp.2012.08.024 10.1016/j.cma.2015.11.013 10.1016/j.na.2013.02.009 10.1002/fld.953 10.1016/j.cma.2005.05.048 10.1007/s00211-005-0632-3 10.1016/j.nonrwa.2012.11.011 10.1016/j.cma.2008.12.001 10.1137/S0036142901385659 10.1002/fld.1650110704 10.1016/j.cma.2006.12.007 10.1007/s10444-004-7640-1 10.1515/jnum-2012-0013 10.1016/0045-7825(95)00844-9 10.1016/j.cam.2007.09.002 10.1002/nme.220 10.1007/s11075-011-9489-y 10.1007/s10915-010-9371-4 10.1016/j.jcp.2009.05.006 10.1016/0898-1221(93)90318-P 10.1016/j.cma.2005.08.016 10.1016/j.cma.2011.11.003 10.1137/S0036142997318164 10.1137/050623942 10.1007/s10915-014-9979-x 10.1137/0733002 10.1016/j.cam.2020.113009 10.1016/j.cam.2014.11.045 10.1016/j.cma.2010.08.008 10.1007/BFb0063447 10.1002/num.20486 10.1016/j.apnum.2017.01.018 10.1016/j.apnum.2019.04.004 10.1016/j.apnum.2017.05.003 10.1137/030601533 10.1016/j.compfluid.2013.03.021 10.1016/j.cam.2009.12.051 10.1051/m2an:1999145 10.1007/978-3-319-45750-5 10.1016/j.cma.2007.11.032 10.1137/070704812 10.1016/0045-7825(89)90111-4
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References	Layton, Lee, Peterson (CR8) 2002; 129 Shang, Qin (CR38) 2016; 300 Shang (CR23) 2013; 233 Shang (CR16) 2020; 381 Li, He, Xu (CR58) 2007; 196 He, Li (CR69) 2009; 198 Zheng, Hou, Shi, Song (CR34) 2009; 228 Zheng, Shang (CR39) 2021; 159 Girault, Raviart (CR2) 1979 Hecht (CR71) 2012; 20 Huang, Feng, He (CR13) 2013; 37 Masud, Khurram (CR32) 2006; 195 Si (CR11) 2012; 59 Shang, Qin (CR6) 2017; 117 Shang, Qin (CR25) 2017; 3 Xu (CR40) 1994; 15 Layton (CR42) 1993; 5 Li (CR57) 2006; 182 Hughes, Mazzei, Oberai (CR30) 2001; 13 He, Liu (CR49) 2006; 25 He (CR47) 2003; 41 CR5 Guermond, Marra, Quartapelle (CR20) 2006; 195 Li, He (CR33) 2008; 214 Adams (CR68) 1975 Labovschii (CR9) 2009; 25 Huang, Feng (CR62) 2013; 14 Zhang, He (CR21) 2010; 234 Zheng, Shan, Hou (CR65) 2010; 26 Gartling (CR73) 1990; 11 Maubach (CR70) 1995; 16 Temam (CR3) 1984 Zheng, Yu, Shi (CR55) 2015; 65 Kaya, Layton, Riviere (CR19) 2006; 44 Qiu (CR60) 2018; 332 Franca, Hughes (CR27) 1993; 105 Shi, Zheng, Yu, Li (CR36) 2014; 38 CR17 Huang, Feng, Liu (CR59) 2012; 62 Li, Shi, Li (CR67) 2019; 42 Wen, He (CR15) 2018; 41 Shang, He, Kim (CR53) 2011; 47 Galvin (CR22) 2011; 200 Franca, Nesliturk (CR46) 2001; 52 Hughes (CR29) 1995; 127 Layton, Lenferink (CR45) 1996; 33 CR50 Erturk, Corke, Gokcol (CR72) 2005; 48 Xu (CR41) 1998; 33 Li, Shi, Li, Chen (CR64) 2019; 470 Layton (CR18) 2002; 133 Shang, Huang (CR24) 2014; 60 He, Mei, Shang, Cui (CR52) 2010; 44 Wang (CR1) 2016; 71 Wang (CR10) 2010; 216 Qiu, Mei (CR63) 2019; 143 Shang (CR37) 2013; 84 Layton, Lee, Peterson (CR44) 1998; 20 Qiu, An, Mei, Xue (CR66) 2017; 120 Shang (CR12) 2013; 79 John, Kaya (CR31) 2005; 26 Girault, Raviart (CR4) 1986 Shang, He (CR54) 2012; 209 CR26 Ervin, Layton, Maubach (CR7) 2000; 37 He, Liu, Sun (CR48) 2005; 101 Brooks, Hughes (CR28) 1982; 32 CR61 Qiu, Mei (CR14) 2015; 280 Dai, Cheng (CR51) 2008; 220 Zheng, Hou, Shi (CR35) 2010; 229 Du, Zuo (CR56) 2018; 75 Layton, Lenferink (CR43) 1998; 35 10101_CR17 WJ Layton (10101_CR45) 1996; 33 YQ Shang (10101_CR37) 2013; 84 HB Zheng (10101_CR34) 2009; 228 V Girault (10101_CR4) 1986 PZ Huang (10101_CR13) 2013; 37 TJR Hughes (10101_CR30) 2001; 13 R Adams (10101_CR68) 1975 YQ Shang (10101_CR53) 2011; 47 JC Xu (10101_CR41) 1998; 33 E Erturk (10101_CR72) 2005; 48 10101_CR61 J Li (10101_CR33) 2008; 214 WJ Layton (10101_CR44) 1998; 20 J Li (10101_CR57) 2006; 182 10101_CR26 YN He (10101_CR49) 2006; 25 KJ Galvin (10101_CR22) 2011; 200 YN He (10101_CR69) 2009; 198 B Zheng (10101_CR39) 2021; 159 YQ Shang (10101_CR25) 2017; 3 YQ Shang (10101_CR16) 2020; 381 YQ Shang (10101_CR38) 2016; 300 A Labovschii (10101_CR9) 2009; 25 LP Franca (10101_CR46) 2001; 52 HL Qiu (10101_CR66) 2017; 120 MH Li (10101_CR64) 2019; 470 10101_CR50 HQ Qiu (10101_CR60) 2018; 332 F Hecht (10101_CR71) 2012; 20 HB Zheng (10101_CR65) 2010; 26 WJ Layton (10101_CR8) 2002; 129 YQ Shang (10101_CR12) 2013; 79 JC Xu (10101_CR40) 1994; 15 DK Gartling (10101_CR73) 1990; 11 J Li (10101_CR58) 2007; 196 YN He (10101_CR52) 2010; 44 S Kaya (10101_CR19) 2006; 44 TJR Hughes (10101_CR29) 1995; 127 J Guermond (10101_CR20) 2006; 195 WJ Layton (10101_CR18) 2002; 133 YN He (10101_CR48) 2005; 101 R Temam (10101_CR3) 1984 V Girault (10101_CR2) 1979 WJ Layton (10101_CR43) 1998; 35 YQ Shang (10101_CR6) 2017; 117 PZ Huang (10101_CR62) 2013; 14 F Shi (10101_CR36) 2014; 38 HL Qiu (10101_CR14) 2015; 280 ZZ Li (10101_CR67) 2019; 42 PZ Huang (10101_CR59) 2012; 62 N Brooks (10101_CR28) 1982; 32 HL Qiu (10101_CR63) 2019; 143 HB Zheng (10101_CR55) 2015; 65 J Maubach (10101_CR70) 1995; 16 A Masud (10101_CR32) 2006; 195 ZY Si (10101_CR11) 2012; 59 Y Zhang (10101_CR21) 2010; 234 HB Zheng (10101_CR35) 2010; 229 VJ Ervin (10101_CR7) 2000; 37 K Wang (10101_CR10) 2010; 216 10101_CR5 V John (10101_CR31) 2005; 26 YQ Shang (10101_CR54) 2012; 209 XX Dai (10101_CR51) 2008; 220 J Wen (10101_CR15) 2018; 41 YN He (10101_CR47) 2003; 41 YQ Shang (10101_CR24) 2014; 60 GZ Du (10101_CR56) 2018; 75 YQ Shang (10101_CR23) 2013; 233 K Wang (10101_CR1) 2016; 71 LP Franca (10101_CR27) 1993; 105 WJ Layton (10101_CR42) 1993; 5
References_xml	– volume: 33 start-page: 1759 year: 1998 end-page: 1777 ident: CR41 article-title: Two-grid discretization techniques for linear and nonlinear PDEs publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142992232949 – volume: 60 start-page: 564 year: 2014 end-page: 583 ident: CR24 article-title: A parallel subgrid stabilized finite element method based on two-grid discretization for simulation of 2D/3D steady incompressible flows publication-title: J. Sci. Comput. doi: 10.1007/s10915-013-9806-9 – volume: 3 start-page: 425 year: 2017 end-page: 444 ident: CR25 article-title: A two-parameter stabilized finite element method for incompressible flows publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.22080 – volume: 42 start-page: 605 year: 2019 end-page: 619 ident: CR67 article-title: Stabilized mixed finite element methods for the Navier-Stokes equations with damping publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.5365 – volume: 332 start-page: 172 year: 2018 end-page: 188 ident: CR60 article-title: Two-grid stabilized methods for the stationary incompressible Navier-Stokes equations with nonlinear slip boundary conditions publication-title: Appl. Math. Comput. – volume: 15 start-page: 231 year: 1994 end-page: 237 ident: CR40 article-title: A novel two-grid method for semilinaer elliptic equations publication-title: SIAM J. Sci. Comput. doi: 10.1137/0915016 – volume: 25 start-page: 1 year: 2009 end-page: 25 ident: CR9 article-title: A defect correction method for the time-dependent Navier-Stokes equations publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20329 – volume: 75 start-page: 1445 year: 2018 end-page: 1462 ident: CR56 article-title: A parallel partition of unity scheme based on two-grid discretizations for the Navier-Stokes problem publication-title: J. Sci. Comput. doi: 10.1007/s10915-017-0593-6 – volume: 13 start-page: 505 year: 2001 end-page: 511 ident: CR30 article-title: The multiscale formulation of large eddy simulation: decay of homogeneous isotropic turbulence publication-title: Phys. Fluids doi: 10.1063/1.1332391 – ident: CR61 – volume: 37 start-page: 728 year: 2013 end-page: 741 ident: CR13 article-title: Two-level defect-correction Oseen iterative stabilized finite element methods for the stationary Navier-Stokes equations publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2012.02.051 – volume: 214 start-page: 58 year: 2008 end-page: 65 ident: CR33 article-title: A stabilized finite element method based on two local Gauss integrations for the Stokes equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.02.015 – volume: 35 start-page: 2035 year: 1998 end-page: 2054 ident: CR43 article-title: A two-level method with backtracking for the Navier-Stokes equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614299630230X – volume: 71 start-page: 120 year: 2016 end-page: 132 ident: CR1 article-title: Iterative schemes for the non-homogeneous Navier-Stokes equations based on the finite element approximation publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2015.11.011 – volume: 38 start-page: 5726 year: 2014 end-page: 5742 ident: CR36 article-title: On the convergence of variational multiscale methods based on Newton’s iteration for the incompressible flows publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2014.04.049 – volume: 47 start-page: 1262 year: 2011 end-page: 1279 ident: CR53 article-title: A new parallel finite element algorithm for the stationary Navier-Stokes equations publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2011.06.001 – volume: 32 start-page: 199 year: 1982 end-page: 259 ident: CR28 article-title: Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(82)90071-8 – volume: 41 start-page: 250 year: 2018 end-page: 260 ident: CR15 article-title: A new defect-correction method for the stationary Navier-Stokes equations based on pressure projection publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4608 – year: 1986 ident: CR4 publication-title: Finite element method for Navier-Stokes equations: theory and algorithms doi: 10.1007/978-3-642-61623-5 – volume: 62 start-page: 988 year: 2012 end-page: 1001 ident: CR59 article-title: Two-level stabilized method based on three corrections for the stationary Navier-Stokes equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2012.03.006 – ident: CR50 – volume: 105 start-page: 285 year: 1993 end-page: 298 ident: CR27 article-title: Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(93)90126-I – volume: 20 start-page: 1 year: 1998 end-page: 12 ident: CR44 article-title: Numerical solution of the stationary Navier-Stokes equations using a multilevel finite element method publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827596306045 – volume: 229 start-page: 7030 year: 2010 end-page: 7041 ident: CR35 article-title: Adaptive finite element variational multiscale method for incompressible flows based on two local Gauss integrations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.05.038 – ident: CR5 – volume: 216 start-page: 3252 year: 2010 end-page: 3264 ident: CR10 article-title: A new defect correction method for the Navier-Stokes equations at high Reynolds numbers publication-title: Appl. Math. Comput. – ident: CR26 – volume: 159 start-page: 138 year: 2021 end-page: 158 ident: CR39 article-title: A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2020.09.001 – year: 1984 ident: CR3 publication-title: Navier-Stokes equations: theory and numerical analysis – volume: 470 start-page: 292 year: 2019 end-page: 307 ident: CR64 article-title: Two-level mixed finite element methods for the Navier-Stokes equations with damping publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.10.002 – volume: 16 start-page: 210 year: 1995 end-page: 227 ident: CR70 article-title: Local bisection refinement for n-simplicial grids generated by reflection publication-title: SIAM J. Sci. Comput. doi: 10.1137/0916014 – volume: 233 start-page: 210 year: 2013 end-page: 226 ident: CR23 article-title: A two-level subgrid stabilized Oseen iterative method for the steady Navier-Stokes equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.08.024 – volume: 300 start-page: 182 year: 2016 end-page: 198 ident: CR38 article-title: A finite element variational multiscale method based on two-grid discretization for the steady incompressible Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2015.11.013 – volume: 84 start-page: 103 year: 2013 end-page: 116 ident: CR37 article-title: A parallel two-level variational multiscale method for the Navier-Stokes equations publication-title: Nonlineal Anal. doi: 10.1016/j.na.2013.02.009 – volume: 48 start-page: 747 year: 2005 end-page: 774 ident: CR72 article-title: Numerical solutions of 2-d steady incompressible driven cavity flow at high Reynolds numbers publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.953 – volume: 195 start-page: 1750 year: 2006 end-page: 1777 ident: CR32 article-title: A multiscale finite element method for the incompressible Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2005.05.048 – volume: 101 start-page: 501 year: 2005 end-page: 522 ident: CR48 article-title: Multi-level spectral Galerkin method for the Navier-Stokes equations I: spatial discretization publication-title: Numer. Math. doi: 10.1007/s00211-005-0632-3 – volume: 14 start-page: 1795 year: 2013 end-page: 1805 ident: CR62 article-title: Two-level stabilized method based on Newton iteration for the steady Smagorinsky model publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2012.11.011 – volume: 198 start-page: 1351 year: 2009 end-page: 1359 ident: CR69 article-title: Convergence of three iterative methods based on the finite element discretization for the stationary Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2008.12.001 – volume: 41 start-page: 1263 year: 2003 end-page: 1285 ident: CR47 article-title: Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142901385659 – volume: 11 start-page: 953 year: 1990 end-page: 967 ident: CR73 article-title: A test problem for outflow boundary conditions-flow over a backward-facing step publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.1650110704 – volume: 196 start-page: 2852 year: 2007 end-page: 2862 ident: CR58 article-title: A multi-level stabilized finite element method for the stationary Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2006.12.007 – volume: 25 start-page: 403 year: 2006 end-page: 433 ident: CR49 article-title: Multi-level spectral Galerkin method for the Navier-Stokes equations, II: time discretization publication-title: Adv. Comput. Math. doi: 10.1007/s10444-004-7640-1 – volume: 20 start-page: 251 year: 2012 end-page: 265 ident: CR71 article-title: New development in FreeFem++ publication-title: J. Numer. Math. doi: 10.1515/jnum-2012-0013 – volume: 127 start-page: 387 year: 1995 end-page: 401 ident: CR29 article-title: Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origins of stabilized methods publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(95)00844-9 – volume: 220 start-page: 566 year: 2008 end-page: 573 ident: CR51 article-title: A two-grid method based on Newton iteration for the Navier-Stokes equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.09.002 – volume: 52 start-page: 433 year: 2001 end-page: 453 ident: CR46 article-title: On a two-level finite element method for the incompressible Navier-Stokes equations publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.220 – volume: 59 start-page: 271 year: 2012 end-page: 300 ident: CR11 article-title: Second order modified method of characteristics mixed defect-correction finite element method for time-dependent Navier-Stokes problems publication-title: Numer. Algor. doi: 10.1007/s11075-011-9489-y – volume: 182 start-page: 140 year: 2006 end-page: 1481 ident: CR57 article-title: Investigations on two kinds of two-level stabilized finite element methods for the stationary Navier-Stokes equations publication-title: Appl. Math. Comput. – volume: 44 start-page: 92 year: 2010 end-page: 106 ident: CR52 article-title: Newton iterative parallel finite element algorithm for the steady Navier-Stokes equations publication-title: J. Sci. Comput. doi: 10.1007/s10915-010-9371-4 – volume: 228 start-page: 5961 year: 2009 end-page: 5977 ident: CR34 article-title: A finite element variational multiscale method for incompressible flows based on two local Gauss integrations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.05.006 – volume: 5 start-page: 33 year: 1993 end-page: 38 ident: CR42 article-title: A two level discretization method for the Navier-Stokes equations publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(93)90318-P – volume: 195 start-page: 5857 year: 2006 end-page: 5876 ident: CR20 article-title: Subgrid stabilized projection method for 2D unsteady flows at high Reynolds numbers publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2005.08.016 – volume: 209 start-page: 172 year: 2012 end-page: 183 ident: CR54 article-title: A parallel Oseen-linearized algorithm for the stationary Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2011.11.003 – volume: 37 start-page: 1165 year: 2000 end-page: 1185 ident: CR7 article-title: Adaptive defect-correction methods for viscous incompressible flow problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142997318164 – volume: 44 start-page: 1639 year: 2006 end-page: 1654 ident: CR19 article-title: Subgrid stabilized defect correction methods for the Navier-Stokes equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/050623942 – ident: CR17 – volume: 65 start-page: 512 year: 2015 end-page: 532 ident: CR55 article-title: Local and parallel finite element method based on the partition of unity for incompressible flow publication-title: J. Sci. Comput. doi: 10.1007/s10915-014-9979-x – year: 1975 ident: CR68 publication-title: Sobolev Spaces – volume: 33 start-page: 17 year: 1996 end-page: 30 ident: CR45 article-title: A multilevel mesh independence principle for the Navier-Stokes equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0733002 – volume: 381 year: 2020 ident: CR16 article-title: A new two-level defect-correction method for the steady Navier-Stokes equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2020.113009 – volume: 280 start-page: 80 year: 2015 end-page: 93 ident: CR14 article-title: Two-level defect-correction stabilized finite element method for Navier-Stokes equations with friction boundary conditions publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.11.045 – volume: 200 start-page: 242 year: 2011 end-page: 250 ident: CR22 article-title: New subgrid artificial viscosity Galerkin methods for the Navier-Stokes equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2010.08.008 – year: 1979 ident: CR2 publication-title: Finite element approximation of the Navier-Stokes equations doi: 10.1007/BFb0063447 – volume: 26 start-page: 1180 year: 2010 end-page: 1190 ident: CR65 article-title: A quadratic equal-order stabilized method for Stokes problem based on two local Gauss integrations publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20486 – volume: 117 start-page: 1 year: 2017 end-page: 21 ident: CR6 article-title: Parallel finite element variational multiscale algorithms for incompressible flow at high Reyonds numbers publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.01.018 – volume: 143 start-page: 188 year: 2019 end-page: 202 ident: CR63 article-title: Multi-level stabilized algorithms for the stationary incompressible Navier-Stokes equations with damping publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2019.04.004 – volume: 129 start-page: 1 year: 2002 end-page: 19 ident: CR8 article-title: A defect-correction method for the incompressible Navier-Stokes equations publication-title: Appl. Math. Comput. – volume: 120 start-page: 97 year: 2017 end-page: 114 ident: CR66 article-title: Two-step algorithms for the stationary incompressible Navier-Stokes equations with friction boundary conditions publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.05.003 – volume: 26 start-page: 1485 year: 2005 end-page: 1503 ident: CR31 article-title: A finite element variational multiscale method for the Navier-Stokes equations publication-title: SIAM J. Sci. Comput. doi: 10.1137/030601533 – volume: 79 start-page: 200 year: 2013 end-page: 212 ident: CR12 article-title: Parallel defect-correction algorithms based on finite element discretization for the Navier-Stokes equations publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2013.03.021 – volume: 234 start-page: 593 year: 2010 end-page: 604 ident: CR21 article-title: Assessment of subgrid-scale models for the incompressible Navier-Stokes equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.12.051 – volume: 133 start-page: 147 year: 2002 end-page: 157 ident: CR18 article-title: A connection between subgrid scale eddy viscosity and mixed methods publication-title: Appl. Math. Comput. – volume: 127 start-page: 387 year: 1995 ident: 10101_CR29 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(95)00844-9 – volume-title: Sobolev Spaces year: 1975 ident: 10101_CR68 – volume: 48 start-page: 747 year: 2005 ident: 10101_CR72 publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.953 – volume: 37 start-page: 1165 year: 2000 ident: 10101_CR7 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142997318164 – ident: 10101_CR17 doi: 10.1051/m2an:1999145 – volume: 33 start-page: 17 year: 1996 ident: 10101_CR45 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0733002 – ident: 10101_CR5 doi: 10.1007/978-3-319-45750-5 – volume-title: Finite element method for Navier-Stokes equations: theory and algorithms year: 1986 ident: 10101_CR4 doi: 10.1007/978-3-642-61623-5 – volume: 117 start-page: 1 year: 2017 ident: 10101_CR6 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.01.018 – volume: 300 start-page: 182 year: 2016 ident: 10101_CR38 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2015.11.013 – volume: 5 start-page: 33 year: 1993 ident: 10101_CR42 publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(93)90318-P – volume: 47 start-page: 1262 year: 2011 ident: 10101_CR53 publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2011.06.001 – volume: 71 start-page: 120 year: 2016 ident: 10101_CR1 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2015.11.011 – volume: 41 start-page: 250 year: 2018 ident: 10101_CR15 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4608 – volume: 38 start-page: 5726 year: 2014 ident: 10101_CR36 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2014.04.049 – volume: 26 start-page: 1485 year: 2005 ident: 10101_CR31 publication-title: SIAM J. Sci. Comput. doi: 10.1137/030601533 – ident: 10101_CR50 doi: 10.1016/j.cma.2007.11.032 – volume: 209 start-page: 172 year: 2012 ident: 10101_CR54 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2011.11.003 – volume: 220 start-page: 566 year: 2008 ident: 10101_CR51 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.09.002 – volume: 332 start-page: 172 year: 2018 ident: 10101_CR60 publication-title: Appl. Math. Comput. – volume: 37 start-page: 728 year: 2013 ident: 10101_CR13 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2012.02.051 – volume: 133 start-page: 147 year: 2002 ident: 10101_CR18 publication-title: Appl. Math. Comput. – volume: 143 start-page: 188 year: 2019 ident: 10101_CR63 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2019.04.004 – volume: 470 start-page: 292 year: 2019 ident: 10101_CR64 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.10.002 – volume: 120 start-page: 97 year: 2017 ident: 10101_CR66 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2017.05.003 – volume: 214 start-page: 58 year: 2008 ident: 10101_CR33 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.02.015 – volume: 65 start-page: 512 year: 2015 ident: 10101_CR55 publication-title: J. Sci. Comput. doi: 10.1007/s10915-014-9979-x – volume: 41 start-page: 1263 year: 2003 ident: 10101_CR47 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142901385659 – volume: 42 start-page: 605 year: 2019 ident: 10101_CR67 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.5365 – ident: 10101_CR61 doi: 10.1137/070704812 – volume: 198 start-page: 1351 year: 2009 ident: 10101_CR69 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2008.12.001 – volume: 60 start-page: 564 year: 2014 ident: 10101_CR24 publication-title: J. Sci. Comput. doi: 10.1007/s10915-013-9806-9 – volume: 196 start-page: 2852 year: 2007 ident: 10101_CR58 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2006.12.007 – volume: 62 start-page: 988 year: 2012 ident: 10101_CR59 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2012.03.006 – volume: 79 start-page: 200 year: 2013 ident: 10101_CR12 publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2013.03.021 – volume: 195 start-page: 5857 year: 2006 ident: 10101_CR20 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2005.08.016 – volume: 20 start-page: 1 year: 1998 ident: 10101_CR44 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827596306045 – volume: 75 start-page: 1445 year: 2018 ident: 10101_CR56 publication-title: J. Sci. Comput. doi: 10.1007/s10915-017-0593-6 – volume: 3 start-page: 425 year: 2017 ident: 10101_CR25 publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.22080 – volume: 229 start-page: 7030 year: 2010 ident: 10101_CR35 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.05.038 – volume: 15 start-page: 231 year: 1994 ident: 10101_CR40 publication-title: SIAM J. Sci. Comput. doi: 10.1137/0915016 – volume: 233 start-page: 210 year: 2013 ident: 10101_CR23 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.08.024 – ident: 10101_CR26 doi: 10.1016/0045-7825(89)90111-4 – volume: 101 start-page: 501 year: 2005 ident: 10101_CR48 publication-title: Numer. Math. doi: 10.1007/s00211-005-0632-3 – volume: 16 start-page: 210 year: 1995 ident: 10101_CR70 publication-title: SIAM J. Sci. Comput. doi: 10.1137/0916014 – volume: 216 start-page: 3252 year: 2010 ident: 10101_CR10 publication-title: Appl. Math. Comput. – volume: 32 start-page: 199 year: 1982 ident: 10101_CR28 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(82)90071-8 – volume: 200 start-page: 242 year: 2011 ident: 10101_CR22 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2010.08.008 – volume: 44 start-page: 92 year: 2010 ident: 10101_CR52 publication-title: J. Sci. Comput. doi: 10.1007/s10915-010-9371-4 – volume-title: Navier-Stokes equations: theory and numerical analysis year: 1984 ident: 10101_CR3 – volume: 159 start-page: 138 year: 2021 ident: 10101_CR39 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2020.09.001 – volume: 25 start-page: 1 year: 2009 ident: 10101_CR9 publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20329 – volume: 105 start-page: 285 year: 1993 ident: 10101_CR27 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/0045-7825(93)90126-I – volume: 13 start-page: 505 year: 2001 ident: 10101_CR30 publication-title: Phys. Fluids doi: 10.1063/1.1332391 – volume: 52 start-page: 433 year: 2001 ident: 10101_CR46 publication-title: Int. J. Numer. Methods Engrg. doi: 10.1002/nme.220 – volume: 26 start-page: 1180 year: 2010 ident: 10101_CR65 publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20486 – volume: 59 start-page: 271 year: 2012 ident: 10101_CR11 publication-title: Numer. Algor. doi: 10.1007/s11075-011-9489-y – volume: 195 start-page: 1750 year: 2006 ident: 10101_CR32 publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2005.05.048 – volume: 20 start-page: 251 year: 2012 ident: 10101_CR71 publication-title: J. Numer. Math. doi: 10.1515/jnum-2012-0013 – volume: 182 start-page: 140 year: 2006 ident: 10101_CR57 publication-title: Appl. Math. Comput. – volume: 35 start-page: 2035 year: 1998 ident: 10101_CR43 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614299630230X – volume: 381 year: 2020 ident: 10101_CR16 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2020.113009 – volume: 14 start-page: 1795 year: 2013 ident: 10101_CR62 publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2012.11.011 – volume: 25 start-page: 403 year: 2006 ident: 10101_CR49 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-004-7640-1 – volume: 129 start-page: 1 year: 2002 ident: 10101_CR8 publication-title: Appl. Math. Comput. – volume: 280 start-page: 80 year: 2015 ident: 10101_CR14 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2014.11.045 – volume: 44 start-page: 1639 year: 2006 ident: 10101_CR19 publication-title: SIAM J. Numer. Anal. doi: 10.1137/050623942 – volume: 84 start-page: 103 year: 2013 ident: 10101_CR37 publication-title: Nonlineal Anal. doi: 10.1016/j.na.2013.02.009 – volume: 228 start-page: 5961 year: 2009 ident: 10101_CR34 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.05.006 – volume-title: Finite element approximation of the Navier-Stokes equations year: 1979 ident: 10101_CR2 doi: 10.1007/BFb0063447 – volume: 234 start-page: 593 year: 2010 ident: 10101_CR21 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.12.051 – volume: 11 start-page: 953 year: 1990 ident: 10101_CR73 publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.1650110704 – volume: 33 start-page: 1759 year: 1998 ident: 10101_CR41 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142992232949
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Snippet	Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step...
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SubjectTerms	Algorithms Boundary conditions Computational Mathematics and Numerical Analysis Computational Science and Engineering Defects Fluid flow High Reynolds number Incompressible flow Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Multiscale analysis Reynolds number Stability analysis Stiffness matrix Visualization
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Title	A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions
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