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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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 418; S. 116470
Hauptverfasser: Guermond, Jean-Luc, Nazarov, Murtazo, Popov, Bojan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.01.2024
Schlagworte:
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
Finite element method
Limiting
Riemann problem
65M60
High-order method
35L45
Invariant domain
65M12
35L65
Hyperbolic systems
ISSN:0045-7825, 1879-2138, 1879-2138
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Zusammenfassung: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.
ISSN:0045-7825
1879-2138
1879-2138
DOI:10.1016/j.cma.2023.116470