An enriched immersed finite element method for interface problems with nonhomogeneous jump conditions

被引：13

作者：

Adjerid, Slimane ^{[1
]}

Babuska, Ivo ^{[2
]}

Guo, Ruchi ^{[3
]}

Lin, Tao ^{[1
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] Univ Texas Austin, ICES, Austin, TX USA

[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2023年 / 404卷

关键词：

Immersed finite elements; Interface problems; Stability; High order approximation; Discontinuous Galerkin method; ELLIPTIC-EQUATIONS; EPITAXIAL-GROWTH; SPACES; PARTITION; APPROXIMATION; BOUNDARIES;

D O I：

10.1016/j.cma.2022.115770

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This article presents the first higher degree immersed finite element (IFE) method with proven optimal convergence for elliptic interface problems with nonhomogeneous jump conditions. It also gives the first analysis for the condition numbers of the resulting systems including the optimal upper bounds with respect to the mesh size and its robustness with respect to small-cut interface elements. In this method, jump conditions are approximated optimally by basic IFE and enrichment IFE which are piecewise pth degree polynomial functions constructed by solving local Cauchy problems on interface elements. The proposed IFE method is based on a discontinuous Galerkin formulation on interface elements and a continuous Galerkin formulation on non-interface elements.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：37

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