The convergence of the bilinear and linear immersed finite element solutions to interface problems

Xiaoming He, Tao Lin, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

42 Citations (Scopus)

Abstract

This article analyzes the error in both the bilinear and linear immersed finite element (IFE) solutions for second-order elliptic boundary problems with discontinuous coefficients. The discontinuity in the coefficients is supposed to happen across general curves, but the mesh of the IFE methods can be allowed not to align with the curve of discontinuity. It has been shown that the bilinear and linear IFE solutions converge to the exact solution under the usual assumptions about the meshes and regularity.
Original languageEnglish
Pages (from-to)312-330
Number of pages19
JournalNumerical Methods for Partial Differential Equations
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • error estimates
  • finite element
  • immersed interface
  • interface problems

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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