Numerical integration over implicitly defined domains for higher order unfitted finite element methods

被引：24

作者：

Olshanskii M.A. ^{[1
]}

Safin D. ^{[1
]}

机构：

[1] Department of Mathematics, University of Houston, Houston, 77204-3008, TX

来源：

Lobachevskii Journal of Mathematics | 2016年 / 37卷 / 5期

基金：

美国国家科学基金会;

关键词：

level set method; moment-fitting; Numerical integration; unfitted finite element methods; XFEM;

D O I：

10.1134/S1995080216050103

中图分类号：

学科分类号：

摘要：

The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment–fitting, local quasi-parametrization and Monte-Carlo techniques. As an application of these techniques, the paper addresses numerical solution of elliptic PDEs posed on domains and manifolds defined implicitly. A higher order unfitted finite element method (FEM) is assumed for the discretization. In such a method the underlying mesh is not fitted to the geometry, and hence the errors of numerical integration over curvilinear elements affect the accuracy of the finite element solution together with approximation errors. The paper studies the numerical complexity of the integration procedures and the performance of unfitted FEMs which employ these tools. © 2016, Pleiades Publishing, Ltd.

引用

页码：582 / 596

页数：14

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