@Article{IJNAM-1-1, author = {Zhang , Zhimin}, title = {Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {1}, pages = {1--24}, abstract = {

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate $O(h^{1+\rho})$ for $\rho = min(\alpha, 1)$, when the mesh is distorted $O(h^{1+\alpha})$ ($\alpha > 0$) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam.OA-2004-1101}, url = {http://global-sci.org/intro/article_detail/ijnam/963.html} }