hp-FEM for second moments of elliptic PDEs with stochastic data

We prove exponential rates of convergence of a class of hp Galerkin Finite Element approximations of solutions to a model tensor non-hypoelliptic equation in the unit square ! = (0, 1) which exhibit singularities on ∂! and on the diagonal ∆ = {(x, y) ∈ ! : x = y}, but are otherwise analytic in !. As we explained in the first part [6] of this work, such problems arise as deterministic second moment equations of linear, second order elliptic operator equations Au = f with Gaussian random field data f .

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