hp-Galerkin for an elliptic stochastic contact problem

Abstract:

We analyse an exterior, elliptic stochastic contact problem where the Neumann data and the gap function are stochastic. We give a mixed formulation for the displacement and the Lagrange multipier representing the traction on the contact boundary in the Signorini Problem. With the tool of the Steklov-Poincare operator we rewrite the problem as a variational inequality which is uniquely solvable in appropriate Sobolev spaces. With a truncated Karhunen-Loeve expansion the problem is transformed into a deterministic but high dimensional one. Using biorthorgonal basis functions a discrete mixed FEM/BEM hp Galerkin scheme is constructed and solved with the semi-smooth Newton's method. A posteriori error estimates are given together with numerical experiments which underline our theoretical results.