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

DOI Web Site 被引用文献4件 参考文献11件 オープンアクセス
  • 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

説明

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.

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