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A Posteriori Finite Element Error Estimation for Diffusion Problems (0)
| Citations: | 15 - 5 self |
BibTeX
@MISC{Adjerid_aposteriori,
author = {Slimane Adjerid and Belkacem Belguendouz and Joseph and Joseph E. Flaherty},
title = {A Posteriori Finite Element Error Estimation for Diffusion Problems},
year = {}
}
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Abstract
Adjerid et al. [2] and Yu [19, 20] show that a posteriori estimates of spatial discretization errors of piecewise bi-p polynomial finite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error estimates are asymptotically correct for other finite element spaces. The key requirement is that the trial space contain all monomial terms of degree p + 1 except for x p+1 1 and x p+1 2 in a Cartesian (x1, x2) frame. Computational results show that the error estimates are accurate, robust, and efficient for a wide range of problems, including some that are not supported by the present theory. These involve quadrilateral-element meshes, problems with singularities, and nonlinear problems.
Keyphrases
diffusion problem posteriori finite element error estimation parabolic problem spatial discretization error finite element space quadrilateral-element mesh present theory monomial term nonlinear problem solution gradient simple error estimate wide range computational result posteriori estimate error estimate square element element vertex trial space contain key requirement
