Localized orthogonal decomposition for a multiscale parabolic stochastic partial differential equation
Journal article, 2024

A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale information on the diffusion. Optimal order strong convergence is derived. The LOD technique is combined with a (multilevel) Monte-Carlo estimator and the weak error is analyzed. Numerical examples that confirm the theoretical findings are provided, and the computational efficiency of the method is highlighted.

Author

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Per Ljung

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Multiscale Modeling and Simulation

1540-3459 (ISSN) 15403467 (eISSN)

Vol. 22 1 205-229

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Subject Categories

Computational Mathematics

Mathematical Analysis

DOI

10.1137/23M1569216

More information

Latest update

7/30/2024