A nonconforming immersed virtual element method for elliptic interface problems

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-09-15 DOI:10.1051/m2an/2023078

Hyeokjoo Park, Do Young Kwak

引用次数: 0

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.

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求解椭圆界面问题的非协调浸入虚元法

本文提出了求解非拟合多边形网格上椭圆界面问题的最低阶非协调浸入虚元法。各界面网格单元上的局部离散空间由具有Neumann边界条件的局部界面问题的解组成，并对椭圆投影进行了修正，使其范围为满足界面条件的破碎线性多项式空间。在分段h2正则性假设下，我们得到了破碎h1范数和l2范数下的最优误差估计。我们方案中的网格假设允许小切割元素，并且不需要额外的网格程序。数值实验验证了理论结果。

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.