Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computations of solutions to elliptic boundary value problems. The proposed method uses a generalized eigenvalue problem to derive the norm estimation. This method has several advantages. Namely, it can be applied to two types of boundary conditions: the Dirichlet type and the Neumann type. It also provides a way of numerically evaluating lower and upper bounds of target eigenvalues. Numerical examples are presented to show that the proposed method provides effective estimations in most cases.
KeywordsEigenvalue problem Elliptic operator Finite element method Inverse norm estimation Numerical verification
Mathematics Subject Classification65N25 65N30 35J25
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