| Issue |
ESAIM: M2AN
Volume 52, Number 4, July-August 2018
|
|
|---|---|---|
| Page(s) | 1533 - 1567 | |
| DOI | https://doi.org/10.1051/m2an/2017012 | |
| Published online | 28 September 2018 | |
Numerical analysis of a nonlinearly stable and positive control volume finite element scheme for Richards equation with anisotropy★
Univ. Lille, CNRS, UMR 8524, Inria — Laboratoire Paul Painlevé, 59000 Lille, France
* Corresponding author: clement.cances@inria.fr
Received:
27
September
2016
Accepted:
15
March
2017
We extend the nonlinear Control Volume Finite Element scheme of [C. Cancès and C. Guichard, Math. Comput. 85 (2016) 549–580]. to the discretization of Richards equation. This scheme ensures the preservation of the physical bounds without any restriction on the mesh and on the anisotropy tensor. Moreover, it does not require the introduction of the so-called Kirchhoff transform in its definition. It also provides a control on the capillary energy. Based on this nonlinear stability property, we show that the scheme converges towards the unique solution to Richards equation when the discretization parameters tend to 0. Finally we present some numerical experiments to illustrate the behavior of the method.
Mathematics Subject Classification: 65M12 / 65M08 / 76S05
Key words: Unsaturated porous media flow / Richards equation / nonlinear discretization / nonlinear stability / convergence analysis
© EDP Sciences, SMAI 2018
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