{"title":"求解椭圆界面问题的非协调浸入虚元法","authors":"Hyeokjoo Park, Do Young Kwak","doi":"10.1051/m2an/2023078","DOIUrl":null,"url":null,"abstract":"This paper presents the lowest-order nonconforming immersed virtual element method for solving elliptic interface problems on unfitted polygonal meshes. The local discrete space on each interface mesh element consists of the solutions of local interface problems with Neumann boundary conditions, and the elliptic projection is modified so that its range is the space of broken linear polynomials satisfying the interface conditions. We derive optimal error estimates in the broken H1-norm and L2-norm, under the piecewise H2regulartiy assumption. The mesh assumptions in our scheme allow small cut elements and do not require additional mesh procedures. Several numerical experiments are provided to confirm the theoretical results.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"14 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A nonconforming immersed virtual element method for elliptic interface problems\",\"authors\":\"Hyeokjoo Park, Do Young Kwak\",\"doi\":\"10.1051/m2an/2023078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents the lowest-order nonconforming immersed virtual element method for solving elliptic interface problems on unfitted polygonal meshes. The local discrete space on each interface mesh element consists of the solutions of local interface problems with Neumann boundary conditions, and the elliptic projection is modified so that its range is the space of broken linear polynomials satisfying the interface conditions. We derive optimal error estimates in the broken H1-norm and L2-norm, under the piecewise H2regulartiy assumption. The mesh assumptions in our scheme allow small cut elements and do not require additional mesh procedures. Several numerical experiments are provided to confirm the theoretical results.\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/m2an/2023078\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/m2an/2023078","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A nonconforming immersed virtual element method for elliptic interface problems
This paper presents the lowest-order nonconforming immersed virtual element method for solving elliptic interface problems on unfitted polygonal meshes. The local discrete space on each interface mesh element consists of the solutions of local interface problems with Neumann boundary conditions, and the elliptic projection is modified so that its range is the space of broken linear polynomials satisfying the interface conditions. We derive optimal error estimates in the broken H1-norm and L2-norm, under the piecewise H2regulartiy assumption. The mesh assumptions in our scheme allow small cut elements and do not require additional mesh procedures. Several numerical experiments are provided to confirm the theoretical 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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