TY - JOUR
T1 - Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals
AU - Zhang , Zhimin
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 1
EP - 24
PY - 2004
DA - 2004/01
SN - 1
DO - http://doi.org/10.4208/ijnam.OA-2004-1101
UR - https://global-sci.org/intro/article_detail/ijnam/963.html
KW - Finite element method, quadrilateral mesh, gradient recovery, superconvergence, a posteriori error estimate.
AB - <p style="text-align: justify;">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 $O(h^{1+\alpha})$ ($\alpha &gt; 0$) from
a regular one. Consequently, the a posteriori error estimator based on
the recovered gradient is asymptotically exact.</p>