Numerical analysis and adaptive computation for solutions of elliptic problems with randomly perturbed coefficients

We develop a reliable efficient method for computing solutions to the Poisson equation a with randomly perturbed coefficient. We assume the perturbation to be piecewise constant and use a non-overlapping domain decomposition algorithm, where the domains coincides with regions where the perturbation is constant, to solve the equations. On each sub-domain we use an truncated Neumann series to approximate the inverse of the local stiffness matrix. By doing so we can solve for all samples simultaneously in a very efficient way. We derive a posteriori error estimates and construct an adaptive algorithm to tune the method parameters automatically. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)