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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations
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by Yoshitaka Watanabe, Takehiko Kinoshita and Mitsuhiro T. Nakao
Math. Comp. 82 (2013), 1543-1557
Published electronically: February 25, 2013


This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of estimate plays an important role in the numerical verification of the solutions for boundary value problems in nonlinear elliptic PDEs. In general, it is not easy to obtain the a priori estimates of the operator norm for inverse elliptic operators. Even if we can obtain these estimates, they are often over estimated. Our proposed a posteriori estimates are based on finite-dimensional spectral norm estimates for the Galerkin approximation and expected to converge to the exact operator norm of inverse elliptic operators. This provides more accurate estimates, and more efficient verification results for the solutions of nonlinear problems.
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Bibliographic Information
  • Yoshitaka Watanabe
  • Affiliation: Research Institute for Information Technology, Kyushu University, Fukuoka 812-8581, Japan
  • Email:
  • Takehiko Kinoshita
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan, Supported by GCOE ‘Fostering top leaders in mathematics’, Kyoto University
  • Email:
  • Mitsuhiro T. Nakao
  • Affiliation: Sasebo National College of Technology, Nagasaki 857-1193, Japan
  • Email:
  • Received by editor(s): May 18, 2011
  • Published electronically: February 25, 2013
  • Additional Notes: This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 20224001, No. 21540134) and supported by Kyoto University Mathematics Global COE Program
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 82 (2013), 1543-1557
  • MSC (2010): Primary 65N30, 35J25; Secondary 65N15, 35B45
  • DOI:
  • MathSciNet review: 3042574