An improvement of the theorem of a posteriori estimates for inverse elliptic operators

• Kinoshita Takehiko

  Center for the Promotion of Interdisciplinary Education and Research, Kyoto University Research Institute for Mathematical Sciences, Kyoto University

• Watanabe Yoshitaka

  Research Institute for Information Technology, Kyushu University

• Nakao Mitsuhiro T.

  Sasebo National College of Technology

抄録

This paper presents a numerical method to verify the invertibility of a linear elliptic operator. The invertibility of a linearized operator is useful information when verifying the existence of a solution for the corresponding nonlinear elliptic partial differential equations (PDEs). The proposed method is proved on the function spaces more suitable than previous methods. The a posteriori estimate, which is expected to converge to the exact operator norm of the inverse elliptic operators, is obtained by less computational cost than existing methods.

収録刊行物

• Nonlinear Theory and Its Applications, IEICE

  Nonlinear Theory and Its Applications, IEICE 5 (1), 47-52, 2014

  一般社団法人 電子情報通信学会

キーワード

• linear elliptic PDEs
• inverse operators
• validated computations

詳細情報

• CRID: 1390001205346454912
• NII論文ID: 130003386652
• DOI: 10.1587/nolta.5.47
• ISSN: 21854106
• Web Site: https://www.jstage.jst.go.jp/article/nolta/5/1/5_47/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可