Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Heiko Berninger - , University of Geneva (Author)
  • Ralf Kornhuber - , Free University of Berlin (Author)
  • Oliver Sander - , Free University of Berlin (Author)

Abstract

We derive and analyze a solver-friendly finite element discretization of a time discrete Richards equation based on Kirchhoff transformation. It can be interpreted as a classical finite element discretization in physical variables with nonstandard quadrature points. Our approach allows for nonlinear outflow or seepage boundary conditions of Signorini type. We show convergence of the saturation and, in the nondegenerate case, of the discrete physical pressure. The associated discrete algebraic problems can be formulated as discrete convex minimization problems and, therefore, can be solved efficiently by monotone multigrid methods. In numerical examples for two and three space dimensions we observe L²-convergence rates of order O(h²) and H¹-convergence rates of order O(h) as well as robust convergence behavior of the multigrid method with respect to extreme choices of soil parameters.

Details

Original languageEnglish
Pages (from-to)2576-2597
JournalSIAM Journal on Numerical Analysis
Volume49
Issue number6
Publication statusPublished - 2011
Peer-reviewedYes
Externally publishedYes

External IDs

Scopus 84856032240
ORCID /0000-0003-1093-6374/work/146644827

Keywords

Library keywords