Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications

Authors:
Mitsuhiro T. Nakao;Kouji Hashimoto
Affiliations:
Faculty of Mathematics, Kyushu University, Fukuoka 812-8581, Japan;Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, we discuss with guaranteed a priori and a posteriori error estimates of finite element approximations for not necessarily coercive linear second order Dirichlet problems. Here, 'guaranteed' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. Using the invertibility condition of concerning elliptic operator, guaranteed a priori and a posteriori error estimates are formulated. This kind of estimates plays essential and important roles in the numerical verification of solutions for nonlinear elliptic problems. Several numerical examples that confirm the actual effectiveness of the method are presented.