Remarks on computable a priori error estimates for finete solution of elliptic ploblems

• Takayasu Akitoshi

  Department of Applied Mathematics, Faculty of Science and Engineering, Waseda University

• Liu Xuefeng

  Research Institute for Science and Engineering, Waseda University

• Oishi Shin'ichi

  Department of Applied Mathematics, Faculty of Science and Engineering, Waseda University CREST/JST

書誌事項

タイトル別名

• Remarks on computable a priori error estimates for finite element solutions of elliptic problems

抄録

For Poisson's equation over a polygonal domain of general shape, the solution of which may have a singularity around re-entrant corners, we provide an explicit a priori error estimate for the approximate solution obtained by finite element methods of high degree. The method used herein is a direct extension of the one developed in preceding paper of the second and third listed authors, which provided a new approach to deal with the singularity by using linear finite elements. In the present paper, we also give a detailed discussion of the dependency of the convergence order on solution singularities, mesh sizes and degrees of the finite element method used.

収録刊行物

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 5 (1), 53-63, 2014

  一般社団法人 電子情報通信学会

キーワード

• Finite element method
• a priori error estimate
• verified numerical computation
• Poisson's equation
• hypercircle equation

詳細情報

• CRID: 1390282680323166464
• NII論文ID: 130003386653
• DOI: 10.1587/nolta.5.53
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/5/1/5_53/_pdf
• 本文言語コード: en
• データソース種別:
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  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可