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A Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BOUHARGUANE, Afaf | |
| hal.structure.identifier | Laboratoire de Mathématiques Nicolas Oresme [LMNO] | |
| dc.contributor.author | SELOULA, Nour El Houda | |
| dc.date.accessioned | 2024-04-04T02:35:24Z | |
| dc.date.available | 2024-04-04T02:35:24Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190635 | |
| dc.description.abstractEn | In 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.iso | en | |
| dc.subject.en | scalar conservation laws | |
| dc.subject.en | convection-diffusion | |
| dc.subject.en | Fractional/nonlocal operator | |
| dc.subject.en | Discontinuous Galerkin method | |
| dc.subject.en | Numerical flux | |
| dc.subject.en | Stability | |
| dc.subject.en | Convergence | |
| dc.subject.en | Numerical simulations | |
| dc.title.en | A Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04023199 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04023199v1 | |
| bordeaux.COinS | ctx_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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