TY - JOUR
T1 - A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
AU - Nakao, M. T.
AU - Hashimoto, K.
AU - Watanabe, Y.
PY - 2005/7
Y1 - 2005/7
N2 - 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.
AB - 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.
KW - Finite element method
KW - Numerical verification
KW - Unique solvability of linear elliptic problem
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U2 - 10.1007/s00607-004-0111-1
DO - 10.1007/s00607-004-0111-1
M3 - Article
AN - SCOPUS:23744514537
VL - 75
SP - 1
EP - 14
JO - Computing
JF - Computing
SN - 0010-485X
IS - 1 SPEC. ISS.
ER -