A Direct Discontinuous Galerkin Method for a High Order Nonlocal Conservation Law
BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
scalar conservation laws
convection-diffusion
Fractional/nonlocal operator
Discontinuous Galerkin method
Numerical flux
Stability
Convergence
Numerical simulations
Origin
Hal imported