{"title":"Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise","authors":"Jiawei Sun, Chi-Wang Shu, Yulong Xing","doi":"10.1051/m2an/2022084","DOIUrl":null,"url":null,"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.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"57 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/m2an/2022084","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.
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