2013.16: A posteriori error estimation for parametric operator equations with applications to PDEs with random data
2013.16: Alex Bespalov, Catherine E. Powell and David Silvester (2013) A posteriori error estimation for parametric operator equations with applications to PDEs with random data.
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Stochastic Galerkin approximation is an increasingly popular approach for the solution of elliptic PDE problems with correlated random data. A typical strategy is to combine conventional ($h$-) finite element approximation on the spatial domain with spectral ($p$-) approximation on a finite-dimensional manifold in the (stochastic) parameter domain. The issues involved in a posteriori error analysis of computed solutions are outlined in this paper. A novel energy error estimator that uses a parameter-free part of the underlying differential operator is introduced which effectively exploits the tensor product structure of the approximation space. We prove that our error estimator is reliable and efficient. We also discuss different strategies for enriching the approximation space and prove two-sided estimates of the error reduction for the corresponding enhanced approximations. These give computable estimates of the error reduction that depend only on the problem data and the original approximation.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||stochastic Galerkin methods, stochastic finite elements, random data, Karhunen-Loeve expansion, parametric operator equations, error estimation, a posteriori error analysis|
|Subjects:||MSC 2000 > 35 Partial differential equations|
MSC 2000 > 65 Numerical analysis
|Deposited By:||Alex Bespalov|
|Deposited On:||14 April 2013|