Numerical analysis of a nonlinearly stable and positive control volume finite element scheme for Richards equation with anisotropy

DOI10.1051/m2an/2017012zbMath1407.65160OpenAlexW2595678453MaRDI QIDQ4613921

Clément Cancès, Ahmed Ait Hammou Oulhaj, Claire Chainais-Hillairet

Publication date: 25 January 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2017012

zbMATH Keywords

convergence analysisnonlinear stabilityRichards equationnonlinear discretizationunsaturated porous media flow

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

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Upstream mobility finite volumes for the Richards equation in heterogenous domains ⋮ Convergence of nonlinear numerical approximations for an elliptic linear problem with irregular data ⋮ A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs ⋮ A posteriori error estimates for the Richards equation ⋮ Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations ⋮ A structure-preserving discontinuous Galerkin scheme for the Fisher-KPP equation ⋮ Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations ⋮ Space-time domain decomposition for two-phase flow between different rock types ⋮ Improving Newton's Method Performance by Parametrization: The Case of the Richards Equation

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