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

Adjerid Slimane; Babuska Ivo; Guo RuchiLin Tao

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

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

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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.

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2023年第1期|1.1-1.37|共37页
作者
Adjerid Slimane; Babuska Ivo; Guo RuchiLin Tao;
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作者单位

Virginia Tech;

Univ Texas Austin;

Univ Calif Irvine;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
中图分类
关键词
Immersed finite elements; Interface problems; Stability; High order approximation; Discontinuous Galerkin method;

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

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