The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations
| Autor: | Nour Seloula, Afaf Bouharguane |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Partial differential equation Differential equation Applied Mathematics 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system Rate of convergence Discontinuous Galerkin method Convergence (routing) Applied mathematics 0101 mathematics [MATH]Mathematics [math] Convection–diffusion equation Linear equation ComputingMilieux_MISCELLANEOUS [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | Applied Numerical Mathematics Applied Numerical Mathematics, Elsevier, 2020, 148, pp.61-78. ⟨10.1016/j.apnum.2019.09.001⟩ |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2019.09.001⟩ |
| Popis: | In this paper, we consider the discontinuous Galerkin method for solving time dependent partial differential equations with convection-diffusion terms and anti-diffusive fractional operator of order α ∈ ( 1 , 2 ) . These equations are motivated by two distinct applications: a dune morphodynamics model and a signal filtering model. The key to study these numerical schemes is to split the anti-diffusive operators into a singular and non-singular integral representations. The problem is then expressed as a system of low order differential equations and a local discontinuous Galerkin method is proposed for these equations. We prove nonlinear stability estimates and optimal order of convergence O ( Δ x k + 1 ) for linear equations and an order of convergence of O ( Δ x k + 1 2 ) for the nonlinear problem. Finally numerical experiments are given to illustrate qualitative behaviors of solutions for both applications and to confirme our convergence results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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