Partially penalized immersed finite element methods for elliptic interface problems

Tao Lin, Yanping Lin, Xu Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

116 Citations (Scopus)

Abstract

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the added penalty, not only can these IFE methods be proven to have the optimal convergence rate in an energy norm provided that the exact solution has sufficient regularity, but also numerical results indicate that their convergence rates in both the H1-norm and the L2-norm do not deteriorate when the mesh becomes finer, which is a shortcoming of the classic IFE methods in some situations. Trace inequalities are established for both linear and bilinear IFE functions that are not only critical for the error analysis of these new IFE methods but are also of a great potential to be useful in error analysis for other related IFE methods.
Original languageEnglish
Pages (from-to)1121-1144
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Immersed finite element
  • Interface problems
  • Optimal convergence

ASJC Scopus subject areas

  • Numerical Analysis

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