Mitsuhiro T. Nakao, Kouji Hashimoto and Yoshitaka Watanabe:
A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems,
Computing, Vol.75, Number 1 (July 2005) pp.1-14.
Special issue: GAMM - Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics. Guest Editor: Jurgen Herzberger.
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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