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Advances in Computational Mathematics

, Volume 43, Issue 4, pp 795–821 | Cite as

Superconvergence of immersed finite element methods for interface problems

  • Waixiang Cao
  • Xu ZhangEmail author
  • Zhimin Zhang
Article

Abstract

In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of generalized orthogonal polynomials that satisfy both orthogonality and interface jump conditions.

Keywords

Superconvergence Immersed finite element method Interface problems Generalized orthogonal polynomials 

Mathematics Subject Classification (2010)

65N30 65N15 35R05 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Beijing Computational Science Research CenterBeijingChina
  2. 2.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA
  3. 3.Department of MathematicsWayne State UniversityDetroitUSA

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