Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642274 | Journal of Computational and Applied Mathematics | 2008 | 10 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mitsuhiro T. Nakao, Kouji Hashimoto,