Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
---|---|---|
Page(s) | 841 - 864 | |
DOI | https://doi.org/10.1051/m2an/2022084 | |
Published online | 30 March 2023 |
Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise
1
Department of Mathematics, The Ohio State University, Columbus OH 43210, USA
2
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
* Corresponding author: xing.205@osu.edu
Received:
12
April
2022
Accepted:
2
October
2022
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.
Mathematics Subject Classification: 65M12 / 65M60 / 65C30 / 35Q61 / 60H35
Key words: Discontinuous Galerkin methods / stochastic Maxwell equations / multiplicative noise / energy law / optimal error estimate
© The authors. Published by EDP Sciences, SMAI 2023
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