The 2-Lagrange Multiplier Method Applied to Nonlinear Transmission Problems for the Richards Equation in Heterogeneous Soil with Cross Points

Research output: Contribution to journalResearch articleContributedpeer-review


  • Heiko Berninger - , University of Geneva (Author)
  • Sébastien Loisel - , Heriot-Watt University (Author)
  • Oliver Sander - , RWTH Aachen University (Author)


We formulate the 2-Lagrange multiplier method for the Richards equation in heterogeneous soil. This allows a rigorous formulation of a discrete version of the Richards equation on subdomain decompositions involving cross points. Using Kirchhoff transformation, the individual subdomain problems can be transformed into convex minimization problems and solved efficiently using a monotone multigrid method. We discuss and compare weak formulations of the time-discrete and fully discretized multidomain problem. It is shown that in the case of two subdomains, when solving the resulting discrete system with a Richardson iteration, the new method is equivalent to a parallel version of the nonlinear Robin method for the Richards equation proposed in [H. Berninger and O. Sander, Comput. Vis. Sci., 13 (2010), pp. 187--205]. We give numerical results for a problem with realistic soil parameters.


Original languageEnglish
Pages (from-to)A2166-A2198
JournalSIAM Journal of Scientific Computing
Issue number5
Publication statusPublished - 2014
Externally publishedYes

External IDs

Scopus 84911446778
ORCID /0000-0003-1093-6374/work/142250576