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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-14 |
| Number of pages | 14 |
| Journal | Computing (Vienna/New York) |
| Volume | 75 |
| Issue number | 1 SPEC. ISS. |
| DOIs | |
| Publication status | Published - 2005 Jul |
| Externally published | Yes |
Keywords
- Finite element method
- Numerical verification
- Unique solvability of linear elliptic problem
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics
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Cite this
Nakao, M. T., Hashimoto, K., & Watanabe, Y. (2005). A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems. Computing (Vienna/New York), 75(1 SPEC. ISS.), 1-14. https://doi.org/10.1007/s00607-004-0111-1