Preprint No.
A-09-03
Heiko Berninger, Oliver Sander
Substructuring of a Signorini-type problem and
Robin's method for the Richards equation in heterogeneous soil
Abstract:
We prove a substructuring result for a variational
inequality concerning - but not restricted to
- the Richards equation in homogeneous soil and including
boundary conditions of Signorini's type. This
generalizes existing results for the linear case and leads
to interface conditions known from linear variational
equalities: continuity of Dirichlet and flux values in a
weak sense. In case of the Richards equation these are
the continuity of the physical pressure and of the water
flux, which is hydrologically reasonable. Therefore, we
also apply these interface conditions in the heterogeneous
case of piecewise constant soil parameters, which
we address by the Robin method. We prove that, for a
certain time discretization, the homogeneous problems
in the subdomains including Robin and Signorini-type
boundary conditions can be solved by convex minimization.
As a consequence we are able to apply monotone
multigrid in the discrete setting as an efficient and robust
solver for the local problems. Numerical results
demonstrate the applicability of our approach.
Keywords:
Domain decomposition methods,
saturated-unsaturated porous media flow, convex
minimization, monotone multigrid
Mathematics Subject Classification (MSC00): 65N12, 65N30, 65N55
Language: ENG
Available: Pr-A-09-03.pdf
Contact: Heiko Berninger, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, D-14195 Berlin, Germany (berninge@math.fu-berlin.de)
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