WIAS Preprint No. 3112, (2024)

A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields


Authors

  • Bachmayr, Markus
  • Eigel, Martin
    ORCID: 0000-0003-2687-4497
  • Eisenmann, Henrik
  • Voulis, Igor

2020 Mathematics Subject Classification

  • 35J25 35R60 41A10 41A63 42C10 65N50 65N30

Keywords

  • Stochastic Galerkin method, finite elements, frame-based error estimation, multilevel expansions of random fields

DOI

10.20347/WIAS.PREPRINT.3112

Abstract

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric variables of solutions. For the corresponding spatial approximations, an independently refined finite element mesh is used for each polynomial coefficient. The method relies on multilevel expansions of input random fields and achieves error reduction with uniform rate. In particular, the saturation property for the refinement process is ensured by the algorithm. The results are illustrated by numerical experiments, including cases with random fields of low regularity.

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