Higher-order XFEM for curved strong and weak discontinuities

Kwok Wah Cheng, Thomas Peter Fries

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The extended finite element method (XFEM) enables the accurate approximation of solutions with jumps or kinks within elements. Optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces. Higher-order convergence for arbitrary curved interfaces relies on two major issues: (i) an accurate quadrature of the Galerkin weak form for the cut elements and (ii) a careful formulation of the enrichment, which should preclude any problems in the blending elements. For (i), we employ a strategy of subdividing the elements into subcells with only one curved side. Reference elements that are higher-order on only one side are then used to map the integration points to the real element. For (ii), we find that enrichments for strong discontinuities are easily extended to higher-order accuracy. In contrast, problems in blending elements may hinder optimal convergence for weak discontinuities. Different formulations are investigated, including the corrected XFEM. Numerical results for several test cases involving strong or weak curved discontinuities are presented. Quadratic and cubic approximations are investigated. Optimal convergence rates are achieved using the standard XFEM for the case of a strong discontinuity. Close-to-optimal convergence rates for the case of a weak discontinuity are achieved using the corrected XFEM.

Original languageEnglish
Pages (from-to)564-590
Number of pages27
JournalInternational journal for numerical methods in engineering
Volume82
Issue number5
DOIs
Publication statusPublished - 30 Apr 2010

Fingerprint

Optimal Convergence Rate
Discontinuity
Higher Order
Strong Discontinuity
Finite element method
High Order Accuracy
Extended Finite Element Method
Formulation
Kink
Approximation
Quadrature
Galerkin
Jump
Numerical Results
Arbitrary

Keywords

  • Corrected XFEM
  • Higher-order accuracy
  • Strong and weak discontinuities
  • XFEM

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

Higher-order XFEM for curved strong and weak discontinuities. / Cheng, Kwok Wah; Fries, Thomas Peter.

In: International journal for numerical methods in engineering, Vol. 82, No. 5, 30.04.2010, p. 564-590.

Research output: Contribution to journalArticleResearchpeer-review

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