A hybridized discontinuous Petrov-Galerkin scheme for scalar conservation laws
SUMMARY We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the i...
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| Vydané v: | International journal for numerical methods in engineering Ročník 91; číslo 9; s. 950 - 970 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Chichester, UK
John Wiley & Sons, Ltd
31.08.2012
Wiley |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | SUMMARY
We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf‐sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propose to enforce this explicitly by introducing a constraint into the local Petrov–Galerkin problem. When the resulting nonlinear system is solved using the Newton–Raphson procedure, the solution inside each element can be locally condensed to yield a global linear system involving only the degrees of freedom of the numerical trace. This results in a significant reduction in memory storage and computation time for the solution of the matrix system, albeit at the cost of solving the local Petrov–Galerkin problems. However, these local problems are independent of each other and thus perfectly scalable. We present several numerical examples to assess the performance of the proposed method. The results show that the HDPG method outperforms the hybridizable discontinuous Galerkin method for problems involving discontinuities. Moreover, for the test case proposed by Peterson, the HDPG method provides optimal convergence of order k + 1. Copyright © 2012 John Wiley & Sons, Ltd. |
|---|---|
| AbstractList | SUMMARY
We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf‐sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propose to enforce this explicitly by introducing a constraint into the local Petrov–Galerkin problem. When the resulting nonlinear system is solved using the Newton–Raphson procedure, the solution inside each element can be locally condensed to yield a global linear system involving only the degrees of freedom of the numerical trace. This results in a significant reduction in memory storage and computation time for the solution of the matrix system, albeit at the cost of solving the local Petrov–Galerkin problems. However, these local problems are independent of each other and thus perfectly scalable. We present several numerical examples to assess the performance of the proposed method. The results show that the HDPG method outperforms the hybridizable discontinuous Galerkin method for problems involving discontinuities. Moreover, for the test case proposed by Peterson, the HDPG method provides optimal convergence of order k + 1. Copyright © 2012 John Wiley & Sons, Ltd. We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf‐sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propose to enforce this explicitly by introducing a constraint into the local Petrov–Galerkin problem. When the resulting nonlinear system is solved using the Newton–Raphson procedure, the solution inside each element can be locally condensed to yield a global linear system involving only the degrees of freedom of the numerical trace. This results in a significant reduction in memory storage and computation time for the solution of the matrix system, albeit at the cost of solving the local Petrov–Galerkin problems. However, these local problems are independent of each other and thus perfectly scalable. We present several numerical examples to assess the performance of the proposed method. The results show that the HDPG method outperforms the hybridizable discontinuous Galerkin method for problems involving discontinuities. Moreover, for the test case proposed by Peterson, the HDPG method provides optimal convergence of order k + 1. Copyright © 2012 John Wiley & Sons, Ltd. |
| Author | Nguyen, N. C. Moro, D. Peraire, J. |
| Author_xml | – sequence: 1 givenname: D. surname: Moro fullname: Moro, D. email: dmoro@mit.edu, D. Moro, 77 Massachusetts Ave. 37-422 Cambridge MA 02139, USA., dmoro@mit.edu organization: Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, MA, Cambridge, USA – sequence: 2 givenname: N. C. surname: Nguyen fullname: Nguyen, N. C. organization: Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, MA, Cambridge, USA – sequence: 3 givenname: J. surname: Peraire fullname: Peraire, J. organization: Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, MA, Cambridge, USA |
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| Cites_doi | 10.1137/070706616 10.1002/(SICI)1097-0363(19990315)29:5<587::AID-FLD805>3.0.CO;2-K 10.1137/S0036142901384162 10.1137/0728006 10.1090/S0025-5718-2010-02410-X 10.2514/6.2010-363 10.1137/070685518 10.2514/6.2011-3228 10.1007/BF02165003 10.1002/nme.2646 10.1007/s10915-010-9359-0 10.1016/j.cma.2009.10.007 10.1137/S0036142997316712 10.1016/j.jcp.2011.05.018 10.1023/A:1012873910884 10.1137/080726653 10.1016/j.jcp.2011.01.035 10.1016/j.cma.2010.01.003 10.1006/jcph.2002.7206 10.1016/j.jcp.2009.01.030 10.1002/nme.1893 10.1016/j.jcp.2009.11.010 10.1016/j.jcp.2010.10.032 10.1016/S0045-7825(98)00359-4 10.1016/j.jcp.2006.01.018 10.1016/j.cma.2004.07.024 10.1016/j.jcp.2009.08.030 10.1137/080728810 10.2514/6.2010-362 10.1002/num.20640 10.1006/jcph.1996.5572 10.1006/jcph.2002.7118 |
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| Keywords | Performance evaluation Discontinuity Costs Constraint nonlinear conservation laws Non linear system Modeling Newton Raphson method Trace Galerkin-Petrov method Computation time Conservation law Linear system Petrov-Galerkin hybridized discontinuous Galerkin Galerkin method Non linear effect Numerical convergence |
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| References | Demkowicz L, Gopalakrishnan J. A class of discontinuous Petrov-Galerkin methods. Part II: optimal test functions. Numerical Methods for Partial Differential Equations 2010; 27(1):70-105. Cockburn B, Gopalakrishnan J, Lazarov R. Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems. SIAM Journal on Numerical Analysis 2009; 47(2):1319-1365. Cockburn B, Dong B, Guzmán J, Restelli M, Sacco R. A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. SIAM Journal on Scientific Computing 2009; 31(5):3827-3846. Nguyen NC, Peraire J, Cockburn B. Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations. Journal of Computational Physics 2011; 230(19):7151-7175. Nguyen NC, Peraire J, Cockburn B. A comparison of HDG methods for Stokes flow. Journal of Scientific Computing 2010; 45:215-237. Cockburn B, Shu C. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Journal of Scientific Computing 2001; 16(3):173-261. Cockburn B, Gopalakrishnan J, Nguyen NC, Peraire J, Sayas F. Analysis of HDG methods for Stokes flow. Mathematics of Computation 2011; 80:723-760. Baumann C, Oden J. A discontinuous HP finite element method for convection-diffusion problems. Computer Methods in Applied Mechanical Engineering 1999; 175(3-4):311-341. Lomtev I, Karniadakis G. A discontinuous Galerkin method for the Navier-Stokes equations. International Journal for Numerical Methods in Engineering 1999; 29(5):587-603. Arnold D, Brezzi F, Cockburn B, Marini L. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis 2002; 39(5):1749-1779. Bassi F, Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. Journal of Computational Physics 1997; 131(2):267-279. Hesthaven J, Warburton T. Nodal high-order methods on unstructured grids: I. Time-domain solution of Maxwell's equations. Journal of Computational Physics 2002; 181(1):186-221. Barter G, Darmofal D. Shock capturing with PDE-based artificial viscosity for DGFEM: part I. Formulation. Journal of Computational Physics 2010; 229(5):1810-1827. Güzey S, Cockburn B, Stolarski HK. The embedded discontinuous Galerkin method: application to linear shell problems. International Journal for Numerical Methods in Engineering 2007; 70(7):757-790. Nguyen NC, Peraire J, Cockburn B. High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Journal of Computational Physics 2011; 230(10):3695-3718. Peraire J, Persson PO. The compact discontinuous Galerkin (CDG) method for elliptic problems. SIAM Journal on Scientific Computing 2008; 30(4):1806-1824. Cockburn B, Shu C. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM Journal on Numerical Analysis 1998; 35(6):2440-2463. Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Journal of Computational Physics 2009; 228(9):3232-3254. Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Journal of Computational Physics 2011; 230(4):1147-1170. Klaij C, Van der Vegt J, Van der Ven H. Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations. Journal of Computational Physics 2006; 217(2):589-611. Demkowicz L, Gopalakrishnan J. A class of discontinuous Petrov-Galerkin methods. Part I: the transport equation. Computer Methods in Applied Mechanical Engineering 2010; 199(23-24):1558-1572. Soon SC, Cockburn B, Stolarski HK. A hybridizable discontinuous Galerkin method for linear elasticity. International Journal for Numerical Methods in Engineering 2009; 80(8):1058-1092. Nguyen NC, Peraire J, Cockburn B. A hybridizable discontinuous Galerkin method for Stokes flow. Computer Methods in Applied Mechanical Engineering 2010; 199(9-12):582-597. Peterson TE. A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM Journal on Numerical Analysis 1991; 28(1):133-140. Cockburn B, Gopalakrishnan J. The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. SIAM Journal on Numerical Analysis 2009; 47:1092-1125. Babuška I. Error-bounds for finite element method. Numerische Mathematik 1971; 16(4):322-333. Hartmann R, Houston P. Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Journal of Computational Physics 2002; 183(2):508-532. Bottasso C, Micheletti S, Sacco R. A multiscale formulation of the discontinuous Petrov-Galerkin method for advective-diffusive problems. Computer Methods in Applied Mechanical Engineering 2005; 194(25-26):2819-2838. Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Journal of Computational Physics 2009; 228(23):8841-8855. 2002; 39 2009; 47 2005; 194 2010; 229 2009; 80 2011 2011; 80 2010 1999; 29 1997; 131 1973 2007; 70 2008; 30 2006; 217 2011; 230 2010; 45 2010; 27 2002; 183 1991; 28 2002; 181 2009; 31 1971; 16 1999; 175 2010; 199 2001; 16 2009; 228 1998; 35 e_1_2_8_28_1 e_1_2_8_29_1 e_1_2_8_24_1 e_1_2_8_26_1 e_1_2_8_27_1 Nguyen NC (e_1_2_8_25_1) 2011 e_1_2_8_3_1 e_1_2_8_2_1 e_1_2_8_5_1 e_1_2_8_4_1 e_1_2_8_7_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_21_1 e_1_2_8_22_1 e_1_2_8_23_1 e_1_2_8_17_1 e_1_2_8_18_1 e_1_2_8_19_1 e_1_2_8_13_1 e_1_2_8_36_1 e_1_2_8_14_1 e_1_2_8_35_1 e_1_2_8_15_1 e_1_2_8_38_1 e_1_2_8_16_1 e_1_2_8_37_1 e_1_2_8_32_1 e_1_2_8_10_1 e_1_2_8_31_1 e_1_2_8_11_1 e_1_2_8_34_1 e_1_2_8_12_1 e_1_2_8_33_1 e_1_2_8_30_1 |
| References_xml | – reference: Babuška I. Error-bounds for finite element method. Numerische Mathematik 1971; 16(4):322-333. – reference: Arnold D, Brezzi F, Cockburn B, Marini L. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis 2002; 39(5):1749-1779. – reference: Nguyen NC, Peraire J, Cockburn B. High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Journal of Computational Physics 2011; 230(10):3695-3718. – reference: Nguyen NC, Peraire J, Cockburn B. Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations. Journal of Computational Physics 2011; 230(19):7151-7175. – reference: Güzey S, Cockburn B, Stolarski HK. The embedded discontinuous Galerkin method: application to linear shell problems. International Journal for Numerical Methods in Engineering 2007; 70(7):757-790. – reference: Barter G, Darmofal D. Shock capturing with PDE-based artificial viscosity for DGFEM: part I. Formulation. Journal of Computational Physics 2010; 229(5):1810-1827. – reference: Cockburn B, Shu C. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Journal of Scientific Computing 2001; 16(3):173-261. – reference: Baumann C, Oden J. A discontinuous HP finite element method for convection-diffusion problems. Computer Methods in Applied Mechanical Engineering 1999; 175(3-4):311-341. – reference: Hesthaven J, Warburton T. Nodal high-order methods on unstructured grids: I. Time-domain solution of Maxwell's equations. Journal of Computational Physics 2002; 181(1):186-221. – reference: Peterson TE. A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM Journal on Numerical Analysis 1991; 28(1):133-140. – reference: Cockburn B, Shu C. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM Journal on Numerical Analysis 1998; 35(6):2440-2463. – reference: Cockburn B, Dong B, Guzmán J, Restelli M, Sacco R. A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. SIAM Journal on Scientific Computing 2009; 31(5):3827-3846. – reference: Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Journal of Computational Physics 2011; 230(4):1147-1170. – reference: Bassi F, Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. Journal of Computational Physics 1997; 131(2):267-279. – reference: Cockburn B, Gopalakrishnan J, Nguyen NC, Peraire J, Sayas F. Analysis of HDG methods for Stokes flow. Mathematics of Computation 2011; 80:723-760. – reference: Klaij C, Van der Vegt J, Van der Ven H. Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations. Journal of Computational Physics 2006; 217(2):589-611. – reference: Peraire J, Persson PO. The compact discontinuous Galerkin (CDG) method for elliptic problems. SIAM Journal on Scientific Computing 2008; 30(4):1806-1824. – reference: Cockburn B, Gopalakrishnan J. The derivation of hybridizable discontinuous Galerkin methods for Stokes flow. SIAM Journal on Numerical Analysis 2009; 47:1092-1125. – reference: Hartmann R, Houston P. Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Journal of Computational Physics 2002; 183(2):508-532. – reference: Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Journal of Computational Physics 2009; 228(23):8841-8855. – reference: Lomtev I, Karniadakis G. A discontinuous Galerkin method for the Navier-Stokes equations. International Journal for Numerical Methods in Engineering 1999; 29(5):587-603. – reference: Nguyen NC, Peraire J, Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Journal of Computational Physics 2009; 228(9):3232-3254. – reference: Demkowicz L, Gopalakrishnan J. A class of discontinuous Petrov-Galerkin methods. Part II: optimal test functions. Numerical Methods for Partial Differential Equations 2010; 27(1):70-105. – reference: Soon SC, Cockburn B, Stolarski HK. A hybridizable discontinuous Galerkin method for linear elasticity. International Journal for Numerical Methods in Engineering 2009; 80(8):1058-1092. – reference: Nguyen NC, Peraire J, Cockburn B. A hybridizable discontinuous Galerkin method for Stokes flow. Computer Methods in Applied Mechanical Engineering 2010; 199(9-12):582-597. – reference: Demkowicz L, Gopalakrishnan J. A class of discontinuous Petrov-Galerkin methods. Part I: the transport equation. Computer Methods in Applied Mechanical Engineering 2010; 199(23-24):1558-1572. – reference: Cockburn B, Gopalakrishnan J, Lazarov R. Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems. SIAM Journal on Numerical Analysis 2009; 47(2):1319-1365. – reference: Nguyen NC, Peraire J, Cockburn B. A comparison of HDG methods for Stokes flow. Journal of Scientific Computing 2010; 45:215-237. – reference: Bottasso C, Micheletti S, Sacco R. A multiscale formulation of the discontinuous Petrov-Galerkin method for advective-diffusive problems. Computer Methods in Applied Mechanical Engineering 2005; 194(25-26):2819-2838. – year: 2011 – volume: 35 start-page: 2440 issue: 6 year: 1998 end-page: 2463 article-title: The local discontinuous Galerkin method for time‐dependent convection–diffusion systems publication-title: SIAM Journal on Numerical Analysis – volume: 16 start-page: 173 issue: 3 year: 2001 end-page: 261 article-title: Runge–Kutta discontinuous Galerkin methods for convection‐dominated problems publication-title: Journal of Scientific Computing – volume: 217 start-page: 589 issue: 2 year: 2006 end-page: 611 article-title: Space–time discontinuous Galerkin method for the compressible Navier–Stokes equations publication-title: Journal of Computational Physics – volume: 47 start-page: 1092 year: 2009 end-page: 1125 article-title: The derivation of hybridizable discontinuous Galerkin methods for Stokes flow publication-title: SIAM Journal on Numerical Analysis – volume: 230 start-page: 7151 issue: 19 year: 2011 end-page: 7175 article-title: Hybridizable discontinuous Galerkin methods for the time‐harmonic Maxwell's equations publication-title: Journal of Computational Physics – volume: 199 start-page: 582 issue: 9‐12 year: 2010 end-page: 597 article-title: A hybridizable discontinuous Galerkin method for Stokes flow publication-title: Computer Methods in Applied Mechanical Engineering – volume: 30 start-page: 1806 issue: 4 year: 2008 end-page: 1824 article-title: The compact discontinuous Galerkin (CDG) method for elliptic problems publication-title: SIAM Journal on Scientific Computing – volume: 230 start-page: 1147 issue: 4 year: 2011 end-page: 1170 article-title: An implicit high‐order hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations publication-title: Journal of Computational Physics – volume: 228 start-page: 3232 issue: 9 year: 2009 end-page: 3254 article-title: An implicit high‐order hybridizable discontinuous Galerkin method for linear convection–diffusion equations publication-title: Journal of Computational Physics – volume: 194 start-page: 2819 issue: 25‐26 year: 2005 end-page: 2838 article-title: A multiscale formulation of the discontinuous Petrov–Galerkin method for advective–diffusive problems publication-title: Computer Methods in Applied Mechanical Engineering – volume: 80 start-page: 1058 issue: 8 year: 2009 end-page: 1092 article-title: A hybridizable discontinuous Galerkin method for linear elasticity publication-title: International Journal for Numerical Methods in Engineering – volume: 29 start-page: 587 issue: 5 year: 1999 end-page: 603 article-title: A discontinuous Galerkin method for the Navier–Stokes equations publication-title: International Journal for Numerical Methods in Engineering – volume: 199 start-page: 1558 issue: 23‐24 year: 2010 end-page: 1572 article-title: A class of discontinuous Petrov‐Galerkin methods. Part I: the transport equation publication-title: Computer Methods in Applied Mechanical Engineering – volume: 230 start-page: 3695 issue: 10 year: 2011 end-page: 3718 article-title: High‐order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics publication-title: Journal of Computational Physics – year: 1973 – volume: 183 start-page: 508 issue: 2 year: 2002 end-page: 532 article-title: Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations publication-title: Journal of Computational Physics – volume: 27 start-page: 70 issue: 1 year: 2010 end-page: 105 article-title: A class of discontinuous Petrov–Galerkin methods. Part II: optimal test functions publication-title: Numerical Methods for Partial Differential Equations – volume: 45 start-page: 215 year: 2010 end-page: 237 article-title: A comparison of HDG methods for Stokes flow publication-title: Journal of Scientific Computing – volume: 181 start-page: 186 issue: 1 year: 2002 end-page: 221 article-title: Nodal high‐order methods on unstructured grids: I. Time‐domain solution of Maxwell's equations publication-title: Journal of Computational Physics – year: 2010 – volume: 80 start-page: 723 year: 2011 end-page: 760 article-title: Analysis of HDG methods for Stokes flow publication-title: Mathematics of Computation – volume: 39 start-page: 1749 issue: 5 year: 2002 end-page: 1779 article-title: Unified analysis of discontinuous Galerkin methods for elliptic problems publication-title: SIAM Journal on Numerical Analysis – volume: 47 start-page: 1319 issue: 2 year: 2009 end-page: 1365 article-title: Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems publication-title: SIAM Journal on Numerical Analysis – start-page: 63 year: 2011 end-page: 84 – volume: 28 start-page: 133 issue: 1 year: 1991 end-page: 140 article-title: A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation publication-title: SIAM Journal on Numerical Analysis – volume: 131 start-page: 267 issue: 2 year: 1997 end-page: 279 article-title: A high‐order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations publication-title: Journal of Computational Physics – volume: 16 start-page: 322 issue: 4 year: 1971 end-page: 333 article-title: Error‐bounds for finite element method publication-title: Numerische Mathematik – volume: 70 start-page: 757 issue: 7 year: 2007 end-page: 790 article-title: The embedded discontinuous Galerkin method: application to linear shell problems publication-title: International Journal for Numerical Methods in Engineering – volume: 228 start-page: 8841 issue: 23 year: 2009 end-page: 8855 article-title: An implicit high‐order hybridizable discontinuous Galerkin method for nonlinear convection–diffusion equations publication-title: Journal of Computational Physics – volume: 229 start-page: 1810 issue: 5 year: 2010 end-page: 1827 article-title: Shock capturing with PDE‐based artificial viscosity for DGFEM: part I. Formulation publication-title: Journal of Computational Physics – volume: 175 start-page: 311 issue: 3‐4 year: 1999 end-page: 341 article-title: A discontinuous HP finite element method for convection–diffusion problems publication-title: Computer Methods in Applied Mechanical Engineering – volume: 31 start-page: 3827 issue: 5 year: 2009 end-page: 3846 article-title: A hybridizable discontinuous Galerkin method for steady‐state convection–diffusion‐reaction problems publication-title: SIAM Journal on Scientific Computing – ident: e_1_2_8_15_1 doi: 10.1137/070706616 – ident: e_1_2_8_12_1 doi: 10.1002/(SICI)1097-0363(19990315)29:5<587::AID-FLD805>3.0.CO;2-K – ident: e_1_2_8_2_1 doi: 10.1137/S0036142901384162 – ident: e_1_2_8_33_1 doi: 10.1137/0728006 – ident: e_1_2_8_37_1 – ident: e_1_2_8_21_1 doi: 10.1090/S0025-5718-2010-02410-X – ident: e_1_2_8_14_1 – ident: e_1_2_8_27_1 doi: 10.2514/6.2010-363 – ident: e_1_2_8_13_1 doi: 10.1137/070685518 – ident: e_1_2_8_30_1 doi: 10.2514/6.2011-3228 – ident: e_1_2_8_35_1 doi: 10.1007/BF02165003 – ident: e_1_2_8_19_1 doi: 10.1002/nme.2646 – ident: e_1_2_8_26_1 doi: 10.1007/s10915-010-9359-0 – ident: e_1_2_8_22_1 doi: 10.1016/j.cma.2009.10.007 – ident: e_1_2_8_6_1 doi: 10.1137/S0036142997316712 – ident: e_1_2_8_28_1 doi: 10.1016/j.jcp.2011.05.018 – ident: e_1_2_8_7_1 doi: 10.1023/A:1012873910884 – ident: e_1_2_8_20_1 doi: 10.1137/080726653 – ident: e_1_2_8_18_1 doi: 10.1016/j.jcp.2011.01.035 – ident: e_1_2_8_8_1 doi: 10.1016/j.cma.2010.01.003 – ident: e_1_2_8_9_1 doi: 10.1006/jcph.2002.7206 – ident: e_1_2_8_16_1 doi: 10.1016/j.jcp.2009.01.030 – ident: e_1_2_8_29_1 doi: 10.1002/nme.1893 – ident: e_1_2_8_3_1 doi: 10.1016/j.jcp.2009.11.010 – start-page: 63 volume-title: Lecture Notes in Computational Science and Engineering year: 2011 ident: e_1_2_8_25_1 – ident: e_1_2_8_23_1 doi: 10.1016/j.jcp.2010.10.032 – ident: e_1_2_8_5_1 doi: 10.1016/S0045-7825(98)00359-4 – ident: e_1_2_8_11_1 doi: 10.1016/j.jcp.2006.01.018 – ident: e_1_2_8_36_1 doi: 10.1016/j.cma.2004.07.024 – ident: e_1_2_8_17_1 doi: 10.1016/j.jcp.2009.08.030 – ident: e_1_2_8_38_1 – ident: e_1_2_8_31_1 doi: 10.1137/080728810 – ident: e_1_2_8_24_1 doi: 10.2514/6.2010-362 – ident: e_1_2_8_32_1 doi: 10.1002/num.20640 – ident: e_1_2_8_4_1 doi: 10.1006/jcph.1996.5572 – ident: e_1_2_8_10_1 doi: 10.1006/jcph.2002.7118 – ident: e_1_2_8_34_1 |
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We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws.... We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time‐dependent scalar conservation laws. The... |
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| SubjectTerms | Classical transport Exact sciences and technology hybridized discontinuous Galerkin Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Nonlinear algebraic and transcendental equations nonlinear conservation laws Numerical analysis Numerical analysis. Scientific computation Partial differential equations, initial value problems and time-dependant initial-boundary value problems Petrov-Galerkin Physics Sciences and techniques of general use Statistical physics, thermodynamics, and nonlinear dynamical systems Transport processes |
| Title | A hybridized discontinuous Petrov-Galerkin scheme for scalar conservation laws |
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