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

10.20347/WIAS.PREPRINT.2753

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.

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