Convergence of adaptive stochastic Galerkin FEM

Alex Bespalov, Dirk Praetorius, Leonardo Rocchi, Michele Ruggeri

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
150 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)2359–2382
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume57
Issue number5
DOIs
Publication statusPublished - 3 Oct 2019

Keywords

  • adaptive methods
  • a posteriori error analysis
  • two-level error estimate
  • stochastic Galerkin methods
  • finite element methods
  • parametric PDEs

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