Some considerations of the invertibility verifications for linear elliptic operators
This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.
KeywordsNumerical verification Solvability of linear problem Differential operators Computer-assisted proof
Mathematics Subject Classification65G20 47F05 35P15
The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 24340018, 23740074, and 24540151).
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