Berninger, H. and Sander, O. (2010) Substructuring of a Signorinitype problem and Robin's method for the Richards equation in heterogeneous soil. Computing and Visualization in Science, 13 (5). pp. 187205. ISSN 14329360

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Official URL: https://dx.doi.org/10.1007/s0079101001415
Abstract
We prove a substructuring result for variational inequalities. It concerns but is not restricted to the Richards equation in heterogeneous soil, and it includes 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. We use these interface conditions in a heterogeneous problem with 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 Signorinitype 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.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1885 
Deposited By:  Ekaterina Engel 
Deposited On:  13 Apr 2016 10:53 
Last Modified:  03 Mar 2017 14:42 
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