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A polynomial chaos approach to stochastic variational inequalities
1*Freie Universität Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin, Germany
Citation Information: Journal of Numerical Mathematics. Volume 18, Issue 4, Pages 235–255, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/jnum.2010.012, December 2010
- Published Online:
We consider stochastic elliptic variational inequalities of the second kind involving a bilinear form with stochastic diffusion coefficient. We prove existence and uniqueness of weak solutions, propose a stochastic Galerkin approximation of an equivalent parametric reformulation, and show equivalence to a related collocation method. Numerical experiments illustrate the efficiency of our approach and suggest similar error estimates as for linear elliptic problems.