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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga
A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga
Mathematics Research Reports
Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.
Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang
Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang
Mathematics Research Reports
A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.
Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang
Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang
Mathematics Research Reports
Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.
A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga
A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga
Mathematics Research Reports
A new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergence at element edge centers for the regular pattern.