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Journal of Scientific Computing

, Volume 79, Issue 1, pp 442–463 | Cite as

A Nonconforming Immersed Finite Element Method for Elliptic Interface Problems

  • Tao Lin
  • Dongwoo Sheen
  • Xu ZhangEmail author
Article
  • 117 Downloads

Abstract

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated-\(Q_1\) nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any stabilization term. Error estimates in energy and \(L^2\)-norms are proved to be better than \(O(h\sqrt{|\log h|})\) and \(O(h^2|\log h|)\), respectively, where the \(|\log h|\) factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.

Keywords

Immersed finite element Nonconforming Rotated-\(Q_1\) Cartesian mesh Elliptic interface problem 

Mathematics Subject Classification

35R05 65N15 65N30 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of Mathematics, and Interdisciplinary Program in Computational Science and TechnologySeoul National UniversitySeoulKorea
  3. 3.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA

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