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Sparse finite element methods for operator equations with stochastic data

Tobias von Petersdorff, Christoph Schwab (2006)

Applications of Mathematics

Let A V V ' be a strongly elliptic operator on a d -dimensional manifold D (polyhedra or boundaries of polyhedra are also allowed). An operator equation A u = f with stochastic data f is considered. The goal of the computation is the mean field and higher moments 1 u V , 2 u V V , ... , k u V V of the solution. We discretize the mean field problem using a FEM with hierarchical basis and N degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment k u for k 1 . The key tool...

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