, Volume 75, Issue 1, pp 1–14

A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems


DOI: 10.1007/s00607-004-0111-1

Cite this article as:
Nakao, M., Hashimoto, K. & Watanabe, Y. Computing (2005) 75: 1. doi:10.1007/s00607-004-0111-1


In this paper, we propose a numerical method to verify the invertibility of second-order linear elliptic operators. By using the projection and the constructive a priori error estimates, the invertibility condition is formulated as a numerical inequality based upon the existing verification method originally developed by one of the authors. As a useful application of the result, we present a new verification method of solutions for nonlinear elliptic problems, which enables us to simplify the verification process. Several numerical examples that confirm the actual effectiveness of the method are presented.

AMS Subject Classifications:



Numerical verificationunique solvability of linear elliptic problemfinite element method

Copyright information

© Springer-Verlag Wien 2005

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Graduate School of MathematicsKyushu UniversityJapan
  3. 3.Computing and Communications CenterKyushu UniversityJapan