Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-03-01 DOI:10.1051/m2an/2022084

Jiawei Sun, Chi-Wang Shu, Yulong Xing

引用次数: 1

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.

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带有乘性噪声的随机Maxwell方程的不连续Galerkin方法

本文提出并分析了具有乘性噪声的一维和二维随机Maxwell方程的有限元不连续Galerkin方法。研究了半离散DG方法的离散能量规律。在一定的网格假设下，得到了半离散方法在一维情况下的最优误差估计，以及在矩形网格和三角形网格两种情况下的最优误差估计。采用强泰勒2.0格式进行时间离散化。给出了一维和二维数值结果，验证了理论分析结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.