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.
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Nakao, M., Hashimoto, K. & Watanabe, Y. A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems. Computing 75, 1–14 (2005). https://doi.org/10.1007/s00607-004-0111-1
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DOI: https://doi.org/10.1007/s00607-004-0111-1