November 2, 2010
|| Prof. Dr. Ralf Kornhuber
Institut fuer Mathematik, Freie Universitaet Berlin
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Richards equations for saturated/unsaturated groundwater flow is basedon state equations relating saturation to capillary pressure.The numerical solution of the resulting degenerate parabolic problemstypically suffers from strong nonlinearities andill-conditioning in the presence of strongly varying saturation.As a remedy, we suggest a solver-friendly discretization based on Kirchhoff transformationwhich can be reinterpreted in physical variables in terms of suitable quadrature rules.In this way ill-conditioning is separated from the numerical solution process.This approach is extended to heterogeneous state equations by domain decompositionmethods based on nonlinear transmission conditions. We show convergence and illustratethe theoretical results by numerical computations.In order to account for uncertain parameters, we consider a polynomial chaos approachto stochastic variational inequalities arising as spatial problemsin time-discretized stochastic versions of Richards equations.