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The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain
Author(s) -
He WenMing,
Cui JunZhi,
Zhu QiDing
Publication year - 2014
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.21881
Subject(s) - superconvergence , mathematics , bounded function , domain (mathematical analysis) , quadratic equation , mathematical analysis , boundary (topology) , finite element method , poisson's equation , partial differential equation , element (criminal law) , symmetrization , geometry , law , physics , thermodynamics , political science
It is the first time for us to combine the local symmetric technique and the weak estimates to investigate the local superconvergence of the finite element method for the Poisson equation in a bounded domain with polygonal boundary where a uniform family of partitions is not required or the solution need not have high global smoothness. Combining a uniform family of triangulations in the interior of domain with a quasiuniform family of triangulations at the boundary of domain, we present a special family of triangulations. By the finite element theory of the derivative of the Green's function presented in this article, we combine the local symmetric technique and the weak estimates to obtain the local superconvergence of the derivative for the quadratic elements. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1854–1876, 2014