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Polynomial preserving recovery for quadratic elements on anisotropic meshes
Author(s) -
Huang Can,
Zhang Zhimin
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20669
Subject(s) - polygon mesh , superconvergence , mathematics , quadratic equation , anisotropy , polynomial , finite element method , estimator , element (criminal law) , geometry , mathematical analysis , physics , statistics , quantum mechanics , thermodynamics , political science , law
Polynomial preserving gradient recovery technique under anisotropic meshes is further studied for quadratic elements. The analysis is performed for highly anisotropic meshes where the aspect ratios of element sides are unbounded. When the mesh is adapted to the solution that has significant changes in one direction but very little, if any, in another direction, the recovered gradient can be superconvergent. The results further explain why recovery type error estimator is robust even under nonstandard and highly distorted meshes. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011