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Some remarks on Zienkiewicz‐Zhu estimator
Author(s) -
Rodríguez Rodolfo
Publication year - 1994
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.1690100509
Subject(s) - mathematics , estimator , polygon mesh , piecewise , finite element method , gravitational singularity , dirichlet problem , boundary (topology) , poisson's equation , dirichlet boundary condition , mathematical analysis , boundary value problem , geometry , statistics , physics , thermodynamics
In this article, Zienkiewicz‐Zhu estimator is analyzed for the piecewise linear finite element approximate solution of an elliptic problem. The estimator is proved to be equivalent to the error for the Poisson equation with a homogeneous Dirichlet boundary condition for any triangular regular mesh. No assumptions are needed about the regularity of the solution (i.e., solutions with corner singularities are not excluded). The estimator is also proved to be asymptotically exact on subdomains where the solution is smooth when parallel meshes are used. Therefore, its behavior is similar to that of other well‐known estimators. © 1994 John Wiley & Sons, Inc.