BOUHARGUANE, Afaf; SELOULA, Nour El Houda

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BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]

SELOULA, Nour El Houda
Laboratoire de Mathématiques Nicolas Oresme [LMNO]

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Document de travail - Pré-publication

Résumé en anglais

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.< Réduire

Mots clés en anglais

scalar conservation laws

convection-diffusion

Fractional/nonlocal operator

Discontinuous Galerkin method

Numerical flux

Stability

Convergence

Numerical simulations

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A Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law

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Résumé en anglais

Mots clés en anglais

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Unités de recherche