• DOI:10.1007/s00607-004-0111-1
• Corpus ID: 18489242

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

@article{Nakao2004ANM,
  title={A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems},
  author={Mitsuhiro T. Nakao and Kouji Hashimoto and Yoshitaka Watanabe},
  journal={Computing},
  year={2004},
  volume={75},
  pages={1-14}
}

• M. Nakao, K. Hashimoto, Y. Watanabe
• Published 1 July 2005
• Mathematics
• Computing

Abstract.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.