Abstract

In this paper we present a high order method to solve the Stokes equations with random coefficients numerically. A stochastic Galerkin approach, based on the truncated KarhunenLoeve decomposition technique for the stochastic inputs, is used to reduce the original stochastic Stokes equations into a set of deterministic equations for the expansion coefficients. Then a spectral collocation method, together with a block Jacobi iteration is applied to solve the resulting problem. The efficiency of the solver is verified in each model problem by numerical tests, against Monte Carlo simulations. Keywords-Random inputs; Wiener-Askey polynomial chaos; Spectral methods; Exponential error convergence

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