Finite difference schemes for the parabolic p-Laplace equation
- Félix del Teso 1
- Erik Lindgren 2
- 1 Departamento de Matematicas, Universidad Autónoma de Madrid (UAM)
- 2 Department of Mathematics, KTH-Royal Institute of Technology, Stockholm
ISSN: 2281-7875
Année de publication: 2023
Volumen: 80
Número: 4
Pages: 527-547
Type: Article
D'autres publications dans: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada
Résumé
We propose a new finite difference scheme for the degenerate parabolic equation ∂tu − div(|∇u|p−2∇u) = f , p ≥ 2. Under the assumption that the data is Hölder continuous, we establish the convergence of the explicit-in-time scheme for the Cauchy problem provided a suitable stability type CFLcondition. An important advantage of our approach, is that the CFL-condition makes use of the regularity provided by the scheme to reduce the computational cost. In particular, for Lipschitz data, the CFL-condition is of the same order as for the heat equation and independent of p.
Information sur le financement
Financeurs
-
Spanish Government
- PGC2018-094522-B-I00
-
Spanish Government
- RYC2020-029589-I
-
Swedish Research Council
- 2017-03736