文章基本信息

标题：On the implementation of the eXtended Finite Element Method (XFEM) for interface problems
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作者：Thomas Carraro ; Sven Wetterauer
期刊名称：Archive of Numerical Software
印刷版ISSN：2197-8263
出版年度：2016
卷号：4
期号：2
语种：English
出版社：Archive of Numerical Software
摘要：The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate quadrature rule; (ii) the shape functions for the extended part of the finite element formulation; (iii) the boundary and interface conditions. We show how to handle the XFEM formulation providing a code that demonstrates the solution of two exemplary interface problems for a strong and a weak discontinuity respectively. In the weak discontinuity case, the loss of conformity due to the blending effect and its remedy are discussed. Furthermore, the optimal convergence of the presented unfitted method is numerically verified.
关键词：Extended Finite Element Method; XFEM; PDE