WIAS Preprint No. 2753, (2020)
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Authors
- Eigel, Martin
- Ernst, Oliver
- Sprungk, Björn
- Tamellini, Lorenzo
2010 Mathematics Subject Classification
- 65D05 65D15 65C30 60H25
Keywords
- Random PDEs, parametric PDEs, a posteriori adaptivity, residual error estimator, convergence, affine diffusion coefficient, sparse grids, stochastic collocation
DOI
Abstract
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting.
Appeared in
- SIAM J. Numer. Anal., 60 (2022), pp. 659--687, DOI 10.1137/20M1364722 .
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