Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 38, Issue 4, Pages A2118-A2140Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1027048
Keywords
stochastic Galerkin methods; stochastic finite elements; PDEs with random data; error estimation; a posteriori error analysis; adaptive methods; parametric operator equations
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This paper is concerned with the design and implementation of efficient solution algorithms for elliptic PDE problems with correlated random data. The energy orthogonality that is built into stochastic Galerkin approximations is cleverly exploited to give an innovative energy error estimation strategy that utilizes the tensor product structure of the approximation space. An associated error estimator is constructed and shown theoretically and numerically to be an effective mechanism for driving an adaptive refinement process. The codes used in the numerical studies are available online.
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