Localized orthogonal decomposition for a multiscale parabolic stochastic partial differential equation
Numerical Analysis
2023-04-28 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2304.14049,
title = {Localized orthogonal decomposition for a multiscale parabolic stochastic partial differential equation},
author = {Annika Lang and Per Ljung and Axel Målqvist},
journal= {arXiv preprint arXiv:2304.14049},
year = {2023}
}