Error estimates for the gradient discretisation of degenerate parabolic equation of porous medium type

Clément Cancès (1) , Jérôme Droniou (2) , Cindy Guichard (3) , Gianmarco Manzini (4) , Manuela Bastidas Olivares , Iuliu Sorin Pop (5)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 Monash University [Melbourne]
3 ANGE - Numerical Analysis, Geophysics and Ecology
4 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche
5 UHasselt - Hasselt University

The gradient discretisation method (GDM) is a generic framework for the spatial discretisation of partial differential equations. The goal of this contribution is to establish an error estimate for a class of degenerate parabolic problems, obtained under very mild regularity assumptions on the exact solution. Our study covers well-known models like the porous medium equation and the fast diffusion equations, as well as the strongly degenerate Stefan problem. Several schemes are then compared in a last section devoted to numerical results.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Clément Cancès, Jérôme Droniou, Cindy Guichard, Gianmarco Manzini, Manuela Bastidas Olivares, et al.. Error estimates for the gradient discretisation of degenerate parabolic equation of porous medium type. Daniele A. Di Pietro; Roland Masson; Luca Formaggia. Polyhedral methods in geosciences, 27, Springer; Springer International Publishing, pp.37-72, 2021, SEMA-SIMAI, ⟨10.1007/978-3-030-69363-3_2⟩. ⟨hal-02540067⟩