Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space
This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a high-order finite element method with an invariant-domain preserving low-order method that uses the closest neighbor sten...
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| Vydané v: | Computer methods in applied mechanics and engineering Ročník 418; s. 116470 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.01.2024
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| ISSN: | 0045-7825, 1879-2138, 1879-2138 |
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| Abstract | This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a high-order finite element method with an invariant-domain preserving low-order method that uses the closest neighbor stencil. The construction of the flux of the low-order method is based on an idea from Abgrall et al. (2017). The mass flux of the low-order and the high-order methods are identical on each finite element cell. This allows for mass preserving and invariant-domain preserving limiting. |
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| AbstractList | This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a high-order finite element method with an invariant-domain preserving low-order method that uses the closest neighbor stencil. The construction of the flux of the low-order method is based on an idea from Abgrall et al. (2017). The mass flux of the low-order and the high-order methods are identical on each finite element cell. This allows for mass preserving and invariant-domain preserving limiting. This paper proposes an invariant-domain preserving approximation technique for nonlinear conservation systems that is high-order accurate in space and time. The algorithm mixes a highorder finite element method with an invariant-domain preserving low-order method that uses the closest neighbor stencil. The construction of the flux of the low-order method is based on an idea from Abgrall et al. (2017). The mass flux of the low-order and the high-order methods are identical on each finite element cell. This allows for mass preserving and invariant-domain preserving limiting. |
| ArticleNumber | 116470 |
| Author | Popov, Bojan Nazarov, Murtazo Guermond, Jean-Luc |
| Author_xml | – sequence: 1 givenname: Jean-Luc orcidid: 0000-0002-6974-6818 surname: Guermond fullname: Guermond, Jean-Luc email: guermond@tamu.edu organization: Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843, USA – sequence: 2 givenname: Murtazo orcidid: 0000-0003-4962-9048 surname: Nazarov fullname: Nazarov, Murtazo organization: Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden – sequence: 3 givenname: Bojan orcidid: 0000-0002-6837-2404 surname: Popov fullname: Popov, Bojan organization: Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843, USA |
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| References | Vilar, Abgrall (b14) 2022 Ricchiuto, Abgrall (b12) 2010; 229 Liu, Tadmor (b6) 1998; 79 Ern, Guermond (b24) 2022; 44 Perthame, Shu (b33) 1996; 73 Guermond, Popov (b3) 2016; 54 Harten, Lax, van Leer (b31) 1983; 25 P.-O. Persson, J. Peraire, Sub-cell shock capturing for discontinuous galerkin methods, in: 44th AIAA Aerospace Sciences Meeting and Exhibit, Number AIAA Paper No. 2015-2006-112 in Aerospace Sciences Meetings, 2006. Kurganov, Petrova, Popov (b44) 2007; 29 Zhang, Shu (b41) 2010; 229 Kuzmin, Quezada de Luna (b25) 2020; 411 Tadmor (b32) 1984; 43 Abgrall, Viville, Beaugendre, Dobrzynski (b4) 2017; 72 Abgrall (b11) 2006; 35 Zhang, Shu (b9) 2011; 230 Guermond, Nazarov (b15) 2014; 272 Guermond, Nazarov, Popov, Yang (b16) 2014; 52 Anderson, Dobrev, Kolev, Kuzmin, Quezada de Luna, Rieben, Tomov (b23) 2017; 334 Sanders (b5) 1988; 51 Kuzmin, Löhner, Turek (b22) 2012 Abgrall (b34) 2018; 18 Harten, Osher (b40) 1987; 24 Kurganov, Petrova (b7) 2001; 88 Quezada De Luna (b2) 2016 Guermond, Nazarov, Popov, Tomas (b17) 2018; 40 Guermond, Popov (b29) 2017; 55 Kuzmin, Turek (b21) 2002; 175 Lax (b30) 1954; 7 A. Jameson, W. Schmidt, E. Turkel, Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, in: 14th AIAA Fluid and Plasma Dynamics Conference, 1981, AIAA Paper 1981–1259. Ern, Guermond (b45) 2021; vol. 72 Khobalatte, Perthame (b38) 1994; 62 Burman (b28) 2007; 47 Zhang, Xia, Shu (b10) 2012; 50 Boris, Book (b19) 1997; 135 Zalesak (b20) 1979; 31 Dafermos (b42) 2010; vol. 325 Kraaijevanger (b36) 1991; 31 Alrashed (b1) 2015 Harten (b39) 1983; 49 Pazner (b8) 2021; 382 Guermond, Popov, Tomas (b18) 2019; 347 Abgrall, Bacigaluppi, Tokareva (b13) 2019; 78 Hoff (b43) 1983; 276 Jameson (b27) 2017; 55 Logg, Mardal, Wells (b35) 2012 Pazner (10.1016/j.cma.2023.116470_b8) 2021; 382 Ern (10.1016/j.cma.2023.116470_b24) 2022; 44 Guermond (10.1016/j.cma.2023.116470_b3) 2016; 54 Zhang (10.1016/j.cma.2023.116470_b10) 2012; 50 Harten (10.1016/j.cma.2023.116470_b31) 1983; 25 Kurganov (10.1016/j.cma.2023.116470_b7) 2001; 88 Vilar (10.1016/j.cma.2023.116470_b14) 2022 10.1016/j.cma.2023.116470_b26 Kuzmin (10.1016/j.cma.2023.116470_b22) 2012 Hoff (10.1016/j.cma.2023.116470_b43) 1983; 276 Dafermos (10.1016/j.cma.2023.116470_b42) 2010; vol. 325 Anderson (10.1016/j.cma.2023.116470_b23) 2017; 334 Kraaijevanger (10.1016/j.cma.2023.116470_b36) 1991; 31 Ricchiuto (10.1016/j.cma.2023.116470_b12) 2010; 229 Logg (10.1016/j.cma.2023.116470_b35) 2012 Quezada De Luna (10.1016/j.cma.2023.116470_b2) 2016 Kuzmin (10.1016/j.cma.2023.116470_b25) 2020; 411 Lax (10.1016/j.cma.2023.116470_b30) 1954; 7 Jameson (10.1016/j.cma.2023.116470_b27) 2017; 55 Tadmor (10.1016/j.cma.2023.116470_b32) 1984; 43 Kurganov (10.1016/j.cma.2023.116470_b44) 2007; 29 Harten (10.1016/j.cma.2023.116470_b40) 1987; 24 Guermond (10.1016/j.cma.2023.116470_b17) 2018; 40 Zalesak (10.1016/j.cma.2023.116470_b20) 1979; 31 Liu (10.1016/j.cma.2023.116470_b6) 1998; 79 Boris (10.1016/j.cma.2023.116470_b19) 1997; 135 Kuzmin (10.1016/j.cma.2023.116470_b21) 2002; 175 Guermond (10.1016/j.cma.2023.116470_b16) 2014; 52 10.1016/j.cma.2023.116470_b37 Zhang (10.1016/j.cma.2023.116470_b9) 2011; 230 Zhang (10.1016/j.cma.2023.116470_b41) 2010; 229 Alrashed (10.1016/j.cma.2023.116470_b1) 2015 Abgrall (10.1016/j.cma.2023.116470_b11) 2006; 35 Perthame (10.1016/j.cma.2023.116470_b33) 1996; 73 Sanders (10.1016/j.cma.2023.116470_b5) 1988; 51 Harten (10.1016/j.cma.2023.116470_b39) 1983; 49 Abgrall (10.1016/j.cma.2023.116470_b13) 2019; 78 Guermond (10.1016/j.cma.2023.116470_b15) 2014; 272 Guermond (10.1016/j.cma.2023.116470_b29) 2017; 55 Abgrall (10.1016/j.cma.2023.116470_b34) 2018; 18 Abgrall (10.1016/j.cma.2023.116470_b4) 2017; 72 Guermond (10.1016/j.cma.2023.116470_b18) 2019; 347 Khobalatte (10.1016/j.cma.2023.116470_b38) 1994; 62 Ern (10.1016/j.cma.2023.116470_b45) 2021; vol. 72 Burman (10.1016/j.cma.2023.116470_b28) 2007; 47 |
| References_xml | – volume: 44 start-page: A3366 year: 2022 end-page: A3392 ident: b24 article-title: Invariant-domain-preserving high-order time stepping: I Explicit Runge-Kutta schemes publication-title: SIAM J. Sci. Comput. – volume: 51 start-page: 535 year: 1988 end-page: 558 ident: b5 article-title: A third-order accurate variation nonexpansive difference scheme for single nonlinear conservation laws publication-title: Math. Comp. – year: 2012 ident: b35 article-title: Automated Solution of Differential Equations By the Finite Element Method – volume: 382 year: 2021 ident: b8 article-title: Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 18 start-page: 327 year: 2018 end-page: 351 ident: b34 article-title: Some remarks about conservation for residual distribution schemes publication-title: Comput. Methods Appl. Math. – volume: 54 start-page: 2466 year: 2016 end-page: 2489 ident: b3 article-title: Invariant domains and first-order continuous finite element approximation for hyperbolic systems publication-title: SIAM J. Numer. Anal. – volume: 175 start-page: 525 year: 2002 end-page: 558 ident: b21 article-title: Flux correction tools for finite elements publication-title: J. Comput. Phys. – year: 2016 ident: b2 article-title: High-Order Maximum Principle Preserving (MPP) Techniques for Solving Conservation Laws with Applications on Multiphase Flow – volume: 78 start-page: 274 year: 2019 end-page: 297 ident: b13 article-title: High-order residual distribution scheme for the time-dependent Euler equations of fluid dynamics publication-title: Comput. Math. Appl. – volume: 272 start-page: 198 year: 2014 end-page: 213 ident: b15 article-title: A maximum-principle preserving publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 43 start-page: 369 year: 1984 end-page: 381 ident: b32 article-title: Numerical viscosity and the entropy condition for conservative difference schemes publication-title: Math. Comp. – volume: 73 start-page: 119 year: 1996 end-page: 130 ident: b33 article-title: On positivity preserving finite volume schemes for Euler equations publication-title: Numer. Math. – volume: 230 start-page: 1238 year: 2011 end-page: 1248 ident: b9 article-title: Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms publication-title: J. Comput. Phys. – volume: 229 start-page: 3091 year: 2010 end-page: 3120 ident: b41 article-title: On maximum-principle-satisfying high order schemes for scalar conservation laws publication-title: J. Comput. Phys. – volume: 31 start-page: 482 year: 1991 end-page: 528 ident: b36 article-title: Contractivity of Runge-Kutta methods publication-title: BIT – volume: 79 start-page: 397 year: 1998 end-page: 425 ident: b6 article-title: Third order nonoscillatory central scheme for hyperbolic conservation laws publication-title: Numer. Math. – year: 2015 ident: b1 article-title: Parallel Multiphase Navier-Stokes Solver – volume: vol. 325 year: 2010 ident: b42 publication-title: Hyperbolic Conservation Laws in Continuum Physics – volume: vol. 72 year: 2021 ident: b45 publication-title: Finite Elements I—Approximation and Interpolation – volume: 7 start-page: 159 year: 1954 end-page: 193 ident: b30 article-title: Weak solutions of nonlinear hyperbolic equations and their numerical computation publication-title: Comm. Pure Appl. Math. – volume: 25 start-page: 35 year: 1983 end-page: 61 ident: b31 article-title: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws publication-title: SIAM Rev. – volume: 88 start-page: 683 year: 2001 end-page: 729 ident: b7 article-title: A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems publication-title: Numer. Math. – volume: 334 start-page: 102 year: 2017 end-page: 124 ident: b23 article-title: High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation publication-title: J. Comput. Phys. – volume: 72 start-page: 1232 year: 2017 end-page: 1268 ident: b4 article-title: Construction of a publication-title: J. Sci. Comput. – volume: 29 start-page: 2381 year: 2007 end-page: 2401 ident: b44 article-title: Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws publication-title: SIAM J. Sci. Comput. – volume: 49 start-page: 151 year: 1983 end-page: 164 ident: b39 article-title: On the symmetric form of systems of conservation laws with entropy publication-title: J. Comput. Phys. – reference: A. Jameson, W. Schmidt, E. Turkel, Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, in: 14th AIAA Fluid and Plasma Dynamics Conference, 1981, AIAA Paper 1981–1259. – volume: 50 start-page: 29 year: 2012 end-page: 62 ident: b10 article-title: Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes publication-title: J. Sci. Comput. – volume: 62 start-page: 119 year: 1994 end-page: 131 ident: b38 article-title: Maximum principle on the entropy and second-order kinetic schemes publication-title: Math. Comp. – volume: 55 start-page: 3120 year: 2017 end-page: 3146 ident: b29 article-title: Invariant domains and second-order continuous finite element approximation for scalar conservation equations publication-title: SIAM J. Numer. Anal. – year: 2012 ident: b22 article-title: Flux-corrected transport: Principles, algorithms, and applications publication-title: Scientific Computation – year: 2022 ident: b14 article-title: A posteriori local subcell correction of high-order discontinuous galerkin scheme for conservation laws on two-dimensional unstructured grids – reference: P.-O. Persson, J. Peraire, Sub-cell shock capturing for discontinuous galerkin methods, in: 44th AIAA Aerospace Sciences Meeting and Exhibit, Number AIAA Paper No. 2015-2006-112 in Aerospace Sciences Meetings, 2006. – volume: 31 start-page: 335 year: 1979 end-page: 362 ident: b20 article-title: Fully multidimensional flux-corrected transport algorithms for fluids publication-title: J. Comput. Phys. – volume: 276 start-page: 707 year: 1983 end-page: 714 ident: b43 article-title: The sharp form of Oleĭnik’s entropy condition in several space variables publication-title: Trans. Amer. Math. Soc. – volume: 52 start-page: 2163 year: 2014 end-page: 2182 ident: b16 article-title: A second-order maximum principle preserving Lagrange finite element technique for nonlinear scalar conservation equations publication-title: SIAM J. Numer. Anal. – volume: 47 start-page: 715 year: 2007 end-page: 733 ident: b28 article-title: On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws publication-title: BIT – volume: 135 start-page: 170 year: 1997 end-page: 186 ident: b19 article-title: Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works publication-title: J. Comput. Phys. – volume: 229 start-page: 5653 year: 2010 end-page: 5691 ident: b12 article-title: Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case publication-title: J. Comput. Phys. – volume: 411 year: 2020 ident: b25 article-title: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws publication-title: J. Comput. Phys. – volume: 24 start-page: 279 year: 1987 end-page: 309 ident: b40 article-title: Uniformly high-order accurate nonoscillatory schemes. I publication-title: SIAM J. Numer. Anal. – volume: 40 start-page: A3211 year: 2018 end-page: A3239 ident: b17 article-title: Second-order invariant domain preserving approximation of the Euler equations using convex limiting publication-title: SIAM J. Sci. Comput. – volume: 347 start-page: 143 year: 2019 end-page: 175 ident: b18 article-title: Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 55 year: 2017 ident: b27 article-title: Origins and further development of the Jameson-Schmidt-Turkel scheme publication-title: AIAA J. – volume: 35 start-page: 641 year: 2006 end-page: 669 ident: b11 article-title: Residual distribution schemes: current status and future trends publication-title: Comput. Fluids – volume: 229 start-page: 5653 issue: 16 year: 2010 ident: 10.1016/j.cma.2023.116470_b12 article-title: Explicit Runge-Kutta residual distribution schemes for time dependent problems: second order case publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.04.002 – volume: 49 start-page: 151 issue: 1 year: 1983 ident: 10.1016/j.cma.2023.116470_b39 article-title: On the symmetric form of systems of conservation laws with entropy publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(83)90118-3 – volume: 50 start-page: 29 issue: 1 year: 2012 ident: 10.1016/j.cma.2023.116470_b10 article-title: Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes publication-title: J. Sci. Comput. doi: 10.1007/s10915-011-9472-8 – ident: 10.1016/j.cma.2023.116470_b37 doi: 10.2514/6.2006-112 – volume: 72 start-page: 1232 issue: 3 year: 2017 ident: 10.1016/j.cma.2023.116470_b4 article-title: Construction of a p-adaptive continuous residual distribution scheme publication-title: J. Sci. Comput. doi: 10.1007/s10915-017-0399-6 – volume: 31 start-page: 335 issue: 3 year: 1979 ident: 10.1016/j.cma.2023.116470_b20 article-title: Fully multidimensional flux-corrected transport algorithms for fluids publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(79)90051-2 – year: 2012 ident: 10.1016/j.cma.2023.116470_b22 article-title: Flux-corrected transport: Principles, algorithms, and applications doi: 10.1007/978-94-007-4038-9 – ident: 10.1016/j.cma.2023.116470_b26 doi: 10.2514/6.1981-1259 – year: 2012 ident: 10.1016/j.cma.2023.116470_b35 – volume: 276 start-page: 707 issue: 2 year: 1983 ident: 10.1016/j.cma.2023.116470_b43 article-title: The sharp form of Oleĭnik’s entropy condition in several space variables publication-title: Trans. Amer. Math. Soc. – volume: 347 start-page: 143 year: 2019 ident: 10.1016/j.cma.2023.116470_b18 article-title: Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2018.11.036 – year: 2016 ident: 10.1016/j.cma.2023.116470_b2 – volume: 7 start-page: 159 year: 1954 ident: 10.1016/j.cma.2023.116470_b30 article-title: Weak solutions of nonlinear hyperbolic equations and their numerical computation publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160070112 – volume: 79 start-page: 397 issue: 3 year: 1998 ident: 10.1016/j.cma.2023.116470_b6 article-title: Third order nonoscillatory central scheme for hyperbolic conservation laws publication-title: Numer. Math. doi: 10.1007/s002110050345 – volume: 43 start-page: 369 issue: 168 year: 1984 ident: 10.1016/j.cma.2023.116470_b32 article-title: Numerical viscosity and the entropy condition for conservative difference schemes publication-title: Math. Comp. doi: 10.1090/S0025-5718-1984-0758189-X – volume: vol. 325 year: 2010 ident: 10.1016/j.cma.2023.116470_b42 – volume: 382 issue: 28 year: 2021 ident: 10.1016/j.cma.2023.116470_b8 article-title: Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 24 start-page: 279 issue: 2 year: 1987 ident: 10.1016/j.cma.2023.116470_b40 article-title: Uniformly high-order accurate nonoscillatory schemes. I publication-title: SIAM J. Numer. Anal. doi: 10.1137/0724022 – volume: 55 issue: 5 year: 2017 ident: 10.1016/j.cma.2023.116470_b27 article-title: Origins and further development of the Jameson-Schmidt-Turkel scheme publication-title: AIAA J. doi: 10.2514/1.J055493 – volume: 55 start-page: 3120 issue: 6 year: 2017 ident: 10.1016/j.cma.2023.116470_b29 article-title: Invariant domains and second-order continuous finite element approximation for scalar conservation equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/16M1106560 – year: 2015 ident: 10.1016/j.cma.2023.116470_b1 – volume: 272 start-page: 198 year: 2014 ident: 10.1016/j.cma.2023.116470_b15 article-title: A maximum-principle preserving C0 finite element method for scalar conservation equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2013.12.015 – volume: 62 start-page: 119 issue: 205 year: 1994 ident: 10.1016/j.cma.2023.116470_b38 article-title: Maximum principle on the entropy and second-order kinetic schemes publication-title: Math. Comp. doi: 10.1090/S0025-5718-1994-1208223-4 – volume: 44 start-page: A3366 issue: 5 year: 2022 ident: 10.1016/j.cma.2023.116470_b24 article-title: Invariant-domain-preserving high-order time stepping: I Explicit Runge-Kutta schemes publication-title: SIAM J. Sci. Comput. doi: 10.1137/21M145793X – volume: 78 start-page: 274 issue: 2 year: 2019 ident: 10.1016/j.cma.2023.116470_b13 article-title: High-order residual distribution scheme for the time-dependent Euler equations of fluid dynamics publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2018.05.009 – volume: 135 start-page: 170 issue: 2 year: 1997 ident: 10.1016/j.cma.2023.116470_b19 article-title: Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works publication-title: J. Comput. Phys. doi: 10.1006/jcph.1997.5756 – volume: 54 start-page: 2466 issue: 4 year: 2016 ident: 10.1016/j.cma.2023.116470_b3 article-title: Invariant domains and first-order continuous finite element approximation for hyperbolic systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/16M1074291 – volume: 52 start-page: 2163 issue: 4 year: 2014 ident: 10.1016/j.cma.2023.116470_b16 article-title: A second-order maximum principle preserving Lagrange finite element technique for nonlinear scalar conservation equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/130950240 – volume: 35 start-page: 641 issue: 7 year: 2006 ident: 10.1016/j.cma.2023.116470_b11 article-title: Residual distribution schemes: current status and future trends publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2005.01.007 – volume: 88 start-page: 683 issue: 4 year: 2001 ident: 10.1016/j.cma.2023.116470_b7 article-title: A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems publication-title: Numer. Math. doi: 10.1007/PL00005455 – volume: 73 start-page: 119 issue: 1 year: 1996 ident: 10.1016/j.cma.2023.116470_b33 article-title: On positivity preserving finite volume schemes for Euler equations publication-title: Numer. Math. doi: 10.1007/s002110050187 – volume: 51 start-page: 535 issue: 184 year: 1988 ident: 10.1016/j.cma.2023.116470_b5 article-title: A third-order accurate variation nonexpansive difference scheme for single nonlinear conservation laws publication-title: Math. Comp. doi: 10.1090/S0025-5718-1988-0935073-3 – volume: 229 start-page: 3091 issue: 9 year: 2010 ident: 10.1016/j.cma.2023.116470_b41 article-title: On maximum-principle-satisfying high order schemes for scalar conservation laws publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.12.030 – volume: 175 start-page: 525 issue: 2 year: 2002 ident: 10.1016/j.cma.2023.116470_b21 article-title: Flux correction tools for finite elements publication-title: J. Comput. Phys. doi: 10.1006/jcph.2001.6955 – volume: 411 issue: 19 year: 2020 ident: 10.1016/j.cma.2023.116470_b25 article-title: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws publication-title: J. Comput. Phys. – volume: 18 start-page: 327 issn: 1609-4840 issue: 3 year: 2018 ident: 10.1016/j.cma.2023.116470_b34 article-title: Some remarks about conservation for residual distribution schemes publication-title: Comput. Methods Appl. Math. doi: 10.1515/cmam-2017-0056 – volume: 25 start-page: 35 issue: 1 year: 1983 ident: 10.1016/j.cma.2023.116470_b31 article-title: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws publication-title: SIAM Rev. doi: 10.1137/1025002 – volume: 31 start-page: 482 issue: 3 year: 1991 ident: 10.1016/j.cma.2023.116470_b36 article-title: Contractivity of Runge-Kutta methods publication-title: BIT doi: 10.1007/BF01933264 – volume: 230 start-page: 1238 issue: 4 year: 2011 ident: 10.1016/j.cma.2023.116470_b9 article-title: Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.10.036 – volume: 47 start-page: 715 issue: 4 year: 2007 ident: 10.1016/j.cma.2023.116470_b28 article-title: On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws publication-title: BIT doi: 10.1007/s10543-007-0147-7 – volume: 29 start-page: 2381 issue: 6 year: 2007 ident: 10.1016/j.cma.2023.116470_b44 article-title: Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws publication-title: SIAM J. Sci. Comput. doi: 10.1137/040614189 – year: 2022 ident: 10.1016/j.cma.2023.116470_b14 – volume: 334 start-page: 102 year: 2017 ident: 10.1016/j.cma.2023.116470_b23 article-title: High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2016.12.031 – volume: 40 start-page: A3211 issue: 5 year: 2018 ident: 10.1016/j.cma.2023.116470_b17 article-title: Second-order invariant domain preserving approximation of the Euler equations using convex limiting publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M1149961 – volume: vol. 72 year: 2021 ident: 10.1016/j.cma.2023.116470_b45 |
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| SubjectTerms | Beräkningsvetenskap med inriktning mot numerisk analys Finite element method High-order method Hyperbolic systems Invariant domain Limiting Riemann problem Scientific Computing with specialization in Numerical Analysis |
| Title | Finite element-based invariant-domain preserving approximation of hyperbolic systems: Beyond second-order accuracy in space |
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