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hal.structure.identifierModeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBOUHARGUANE, Afaf
hal.structure.identifierLaboratoire de Mathématiques Nicolas Oresme [LMNO]
dc.contributor.authorSELOULA, Nour El Houda
dc.date.accessioned2024-04-04T02:35:24Z
dc.date.available2024-04-04T02:35:24Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190635
dc.description.abstractEnIn this paper, we develop a Direct Discontinuous Galerkin (DDG) method for solving a time dependent partial differential equation with convection-diffusion terms and a nonlocal term which is a pseudo-differential operator of order α ∈ (1, 2). This kind of equation was first introduced to describe morphodynamics of dunes and was then used for signal processing methods. We consider the DDG method which is based on the direct weak formulation of the PDE into the DG function space for both numerical solution and test functions. Suitable numerical fluxes for all operators are then introduced. We prove nonlinear stability estimates along with convergence results. Finally numerical experiments are given to illustrate qualitative behaviors of solutions and to confirm convergence results.
dc.language.isoen
dc.subject.enscalar conservation laws
dc.subject.enconvection-diffusion
dc.subject.enFractional/nonlocal operator
dc.subject.enDiscontinuous Galerkin method
dc.subject.enNumerical flux
dc.subject.enStability
dc.subject.enConvergence
dc.subject.enNumerical simulations
dc.title.enA Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04023199
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04023199v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BOUHARGUANE,%20Afaf&SELOULA,%20Nour%20El%20Houda&rft.genre=preprint


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