Year: 2005
Author: Mark Ainsworth
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 1 : pp. 1–18
Abstract
We derive an a posteriori error estimator giving a computable upper bound on the error in the energy norm for finite element approximation using the non-conforming rotated $\mathbb{Q}_1$ finite element. It is shown that the estimator also gives a local lower bound up to a generic constant. The bounds do not require additional assumptions on the regularity of the true solution of the underlying elliptic problem and, the mesh is only required to be locally quasi-uniform and may consist of general, non-affine convex quadrilateral elements.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-916
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 1 : pp. 1–18
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: a posteriori error estimation non-conforming finite elements rotated $\mathbb{Q}_1$ element non-affine quadrilateral elements.