Approximation capabilities of immersed finite element spaces for elasticity Interface problems

Ruchi Guo, Tao Lin, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear, and rotated Q 1 polynomials for solving planar elasticity equation involving interface. The shape functions in these IFE spaces are constructed through a group of approximate jump conditions such that the unisolvence of the bilinear and rotated Q 1 IFE shape functions are always guaranteed regardless of the Lamé parameters and the interface location. The boundedness property and a group of identities of the proposed IFE shape functions are established. A multi-point Taylor expansion is utilized to show the optimal approximation capabilities for the proposed IFE spaces through the Lagrange type interpolation operators.

Original languageEnglish
Pages (from-to)1243-1268
Number of pages26
JournalNumerical Methods for Partial Differential Equations
Volume35
Issue number3
DOIs
Publication statusPublished - May 2019

Keywords

  • discontinuous coefficients
  • elasticity equations
  • immersed finite element method
  • interface problems

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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