Journal
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
Volume 6, Issue 1, Pages 243-272Publisher
SIAM PUBLICATIONS
DOI: 10.1137/17M1139928
Keywords
stochastic Galerkin methods; stochastic finite elements; PDEs with random data; adaptive methods; a posteriori error estimation; singularities; parametric PDEs
Funding
- EPSRC [EP/P013791/1]
- EPSRC [EP/P013791/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/P013791/1] Funding Source: researchfish
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We present a novel adaptive algorithm implementing the stochastic Galerkin finite element method for numerical solution of elliptic PDE problems with correlated random data. The algorithm employs a hierarchical a posteriori error estimation strategy which also provides effective estimates of the error reduction for enhanced approximations. These error reduction indicators are used in the algorithm to perform a balanced adaptive refinement of spatial and parametric components of Galerkin approximations. The results of numerical tests demonstrating the efficiency of the algorithm for three representative PDEs with random coefficients are reported. The software used for numerical experiments is available online.
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