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.
- Finite element method
- Numerical verification
- Unique solvability of linear elliptic problem
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics