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AuthorSlimane Adjerid, Belkacem Belguendouz and Joseph E. Flaherty
TitleA Posteriori Finite Element Error Estimation for Diffusion Problems
Year1996
JournalSIAM Journal on Scientific Computing
Volume21(2)
Pages728-746
AbstractWe consider a posteriori estimates of spatial discretization errors of pth order finite element solutions of two-dimensional elliptic and parabolic problems on meshes of rectangular elements. We show that error estimates for piecewise bi-p polynomial spaces obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even extend to other solution spaces. In particular, we establish that these error estimates converge at the same rate as the actual error for finite element spaces that contain all two-dimensional monomial terms of order except for and in a Cartesian frame with coordinates . Computational results show that the error estimates are accurate and robust for a wide range of problems, including some that are not supported by the present theory. These involve quadrilateral-element meshes, singularities, and nonlinearity.
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