Correction of incompleteness of XFEM approximation (1st report: General formulation and theoretical error analyses)

Kazuki Shibanuma, Tomoaki Utsunomiya, Shuji Aihara

Research output: Contribution to journalArticle

Abstract

The XFEM is a numerical method which employs the local enrichment considering a priori knowledge of the solution in the framework of the FEM. The XFEM has an essential problem in the approximation of the partially enriched 'blending elements', which causes a lack of accuracy. Using the weighted XFEM, the numerical accuracy was effectively improved for the problem. It was however found that the influence of the blending elements still remains by the detailed examination in the numerical results. In the present paper, the incompleteness of the weighted XFEM is proved through a theoretical error analysis. Then, a 'PU-XFEM' is proposed in order to correct the incompleteness in the existing XFEM approximations. The PU-XFEM is formulated as the exact development of the PUFEM with local enrichment. As a result of the error analysis, it is found that the PU-XFEM is a proper XFEM without problem of the blending elements.

Original languageEnglish
Article number20110004
JournalTransactions of the Japan Society for Computational Engineering and Science
Volume2011
Issue numberA
Publication statusPublished - 2011
Externally publishedYes

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Error analysis
Numerical methods
Finite element method

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Engineering(all)

Cite this

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abstract = "The XFEM is a numerical method which employs the local enrichment considering a priori knowledge of the solution in the framework of the FEM. The XFEM has an essential problem in the approximation of the partially enriched 'blending elements', which causes a lack of accuracy. Using the weighted XFEM, the numerical accuracy was effectively improved for the problem. It was however found that the influence of the blending elements still remains by the detailed examination in the numerical results. In the present paper, the incompleteness of the weighted XFEM is proved through a theoretical error analysis. Then, a 'PU-XFEM' is proposed in order to correct the incompleteness in the existing XFEM approximations. The PU-XFEM is formulated as the exact development of the PUFEM with local enrichment. As a result of the error analysis, it is found that the PU-XFEM is a proper XFEM without problem of the blending elements.",
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AU - Shibanuma, Kazuki

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AU - Aihara, Shuji

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