Convergence of adaptive stochastic Galerkin FEM

Abstract

We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite element approximations. The algorithms are driven by the energy error reduction estimates derived from two-level a posteriori error indicators for spatial approximations and hierarchical a posteriori error indicators for parametric approximations. The focus of this work is on the mathematical foundation of the adaptive algorithms in the sense of rigorous convergence analysis. In particular, we prove that the proposed algorithms drive the underlying energy error estimates to zero.

References in corpus (2)

• Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
• Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations

Cited by in corpus (7)

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• Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs
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• A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case
• Error estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation
• An Adaptive Algorithm Based on Stochastic Discontinuous Galerkin for Convection Dominated Equations with Random Data