Optimal Finite Element Methods for Interface Problems

  • Jinchao XuEmail author
  • Shuo Zhang
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


There are many physical problems such as multiphase flows and fluid-structure interactions whose solutions are piecewise smooth but may have discontinuity across some curved interfaces. The direct application of standard finite element method may not perform well. In this paper, we study some special finite element methods for this type of problems. For simplicity of exposition, we consider the case that there is only one interface which is smooth. Let \(\varOmega,\varOmega _{1} \subset \mathbb{R}^{2}\) be two bounded domains with \(\varOmega _{1} \subset \varOmega\). We assume that Γ = ∂ Ω1 is sufficiently smooth, and \(\varGamma \cap \partial \varOmega =\emptyset\). To be focused on the influence of Γ, we assume \(\varOmega = (-1,1)^{2}\).


Element Space Multigrid Method Linear Element Interpolation Operator Piecewise Smooth Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Dr. Xiaozhe Hu for his help on the numerical examples.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Computational Mathematics and ApplicationsThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.LSEC, ICMSEC, NCMIS, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina

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