Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise

TL;DR

This paper develops and analyzes finite element discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise, providing error estimates and validating results through numerical experiments.

Contribution

It introduces novel DG methods for stochastic Maxwell equations with multiplicative noise, including error analysis and validation for 1D and 2D cases.

Findings

Optimal error estimates achieved for 1D and 2D cases

Discrete energy law established for semi-discrete methods

Numerical results confirm theoretical analysis

Abstract

In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were studied. Optimal error estimate of the semi-discrete method is obtained for the one-dimensional case, and the two-dimensional case on both rectangular meshes and triangular meshes under certain mesh assumptions. Strong Taylor 2.0 scheme is used as the temporal discretization. Both one- and two-dimensional numerical results are presented to validate the theoretical analysis results.