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Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Stepping

hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorMICHEL, Sixtine
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorTORLO, Davide
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorRICCHIUTO, Mario
hal.structure.identifierUniversität Zürich [Zürich] = University of Zurich [UZH]
hal.structure.identifierCertified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]
dc.contributor.authorABGRALL, Rémi
dc.date.accessioned2024-04-04T02:43:01Z
dc.date.available2024-04-04T02:43:01Z
dc.date.issued2021-11
dc.identifier.issn0885-7474
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191299
dc.description.abstractEnWe study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of the CFL number and of the stabilization parameters involved in different types of stabilization operators. In particular, we analyze the streamline-upwind Petrov-Galerkin (SUPG) stabilization technique, the continuous interior penalty (CIP) stabilization method and the local projection stabilization (LPS). Three different choices for the continuous finite element space are compared: Bernstein polynomials, Lagrangian polynomials on equispaced nodes, and Lagrangian polynomials on Gauss-Lobatto cubature nodes. For the last choice, we only consider inexact quadrature based on the formulas corresponding to the degrees of freedom of the element, which allows to obtain a fully diagonal mass matrix. We also compare different time stepping strategies, namely Runge-Kutta (RK), strong stability preserving RK (SSPRK) and deferred correction time integration methods. The latter allows to alleviate the computational cost as the mass matrix inversion is replaced by the high order correction iterations. To understand the effects of these choices, both time-continuous and fully discrete Fourier analysis are performed. These allow to compare all the different combinations in terms of accuracy and stability, as well as to provide suggestions for optimal values discretization parameters involved. The results are thoroughly verified numerically both on linear and non-linear problems, and error-CPU time curves are provided. Our final conclusions suggest that cubature elements combined with SSPRK and CIP or LPS stabilization are the most promising combinations.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enContinuous Galerkin method
dc.subject.enSpectral element method
dc.subject.enStreamline Upwind Petrov-Galerkin
dc.subject.enLocal Projection Stabilization
dc.subject.enContinuous Interior Penalty
dc.subject.enDispersion analysis
dc.subject.encubature nodes
dc.subject.enFekete nodes
dc.subject.enDeferred Correction scheme MSC: 65M60
dc.title.enSpectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Stepping
dc.typeArticle de revue
dc.identifier.doi10.1007/s10915-021-01632-7
dc.subject.halInformatique [cs]/Modélisation et simulation
bordeaux.journalJournal of Scientific Computing
bordeaux.volume89
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03508353
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03508353v1
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