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
Hlavní autori:	Guermond, Jean-Luc, Nazarov, Murtazo, Popov, Bojan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.01.2024
Predmet:	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
On-line prístup:	Získať plný text
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Popis
Shrnutí:	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