Error estimates for a partially penalized immersed finite element method for elasticity interface problems

Ruchi Guo, Tao Lin (Corresponding Author), Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

This article is about the error analysis for a partially penalized immersed finite element (PPIFE) method designed to solve linear planar-elasticity problems whose Lamé parameters are piecewise constants with an interface-independent mesh. The bilinear form in this method contains penalties to handle the discontinuity in the global immersed finite element (IFE) functions across interface edges. We establish a stress trace inequality for IFE functions on interface elements, we employ a patch idea to derive an optimal error bound for the stress of the IFE interpolation on interface edges, and we design a suitable energy norm by which the bilinear form in this PPIFE method is coercive. These key ingredients enable us to prove that this PPIFE method converges optimally in both an energy norm and the usual L2 norm under the standard piecewise H2-regularity assumption for the exact solution. Features of the proposed PPIFE method are demonstrated with numerical examples.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume54
Issue number1
DOIs
Publication statusPublished - 14 Jan 2020

Keywords

  • Discontinuous Lamé parameters
  • Elasticity systems
  • Immersed finite element methods
  • Interface problems

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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