A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems
First Online: 24 March 2005 Received: 03 November 2003 Revised: 18 June 2004 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 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. AMS Subject Classifications: 35J25 35J60 65N25 Keywords Numerical verification unique solvability of linear elliptic problem finite element method References
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