Volume 56, Number 6, November-December 2022
|Page(s)||1955 - 1992|
|Published online||14 September 2022|
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
2 Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18, 37083 Göttingen, Germany
* Corresponding author: firstname.lastname@example.org
Accepted: 10 July 2022
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline wavelet approximation in the spatial variables. Relying on a multilevel expansion of the given random diffusion coefficient, the method is shown to achieve optimal computational complexity up to a logarithmic factor. In contrast to existing results, this holds in particular when the achievable convergence rate is limited by the regularity of the random field, rather than by the spatial approximation order. The convergence and complexity estimates are illustrated by numerical experiments.
Mathematics Subject Classification: 35J25 / 35R60 / 41A10 / 41A25 / 41A63 / 42C10 / 65D99 / 65N50 / 65T60
Key words: Parameter-dependent elliptic partial differential equations / stochastic Galerkin method / a posteriori error estimation / adaptive methods / complexity analysis
© The authors. Published by EDP Sciences, SMAI 2022
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