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Error estimation and adaptive computation forelliptic problems with randomly perturbed coefficients

Axel Malqvist
UCSD Department of Mathematics


We develop and analyze an efficient numerical method for computingthe response of the solution of an elliptic problem with randomlyperturbed coefficients. We use a variational analysis based on the adjointoperator to deal with the perturbations in data. To deal withperturbations in the diffusion coefficient, we construct a piecewiseconstant approximation to the random perturbation then use domaindecomposition to decompose the problem into sub-problems on whichthe diffusion coefficient is constant. To compute local solutions ofthe sub-problems, we use the infinite series for the inverse of aperturbation of an invertible matrix to devise a fast way to computethe effects of variation in the parameter. Finally, we derive aposteriori error estimates that take into account all the sourcesof error and derive a new adaptive algorithm that provides aquantitative way to distribute computational resources between allof the sources.

Tuesday, November 7, 2006
11:00AM AP&M 2402