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Finite difference schemes for the parabolic p-Laplace equation

Author
del Teso, Félix; Lindgren, Erik
Entity
UAM. Departamento de Matemáticas
Publisher
Springer
Date
2022-10-21
Citation
10.1007/s40324-022-00316-y
SeMA Journal (2022): 1-21
 
 
 
ISSN
2254-3902 (print); 2281-7875 (online)
DOI
10.1007/s40324-022-00316-y
Funded by
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature
Editor's Version
https://doi.org/10.1007/s40324-022-00316-y
Subjects
Explicit scheme; Finite differences; Mean value property; p-Laplacian; Viscosity solutions; Matemáticas
URI
http://hdl.handle.net/10486/705324
Rights
© The Author(s) 2022

Licencia Creative Commons
Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.

Abstract

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 CFL-condition. 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
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