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Natural superconvergent points of triangular finite elements
Author(s) -
Lin Runchang,
Zhang Zhimin
Publication year - 2004
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.20013
Subject(s) - superconvergence , mathematics , laplace's equation , partial differential equation , finite element method , function (biology) , polynomial , laplace transform , poisson's equation , discrete poisson equation , mathematical analysis , poisson distribution , symmetry (geometry) , geometry , statistics , evolutionary biology , biology , thermodynamics , physics
Abstract In this work, we analytically identify natural superconvergent points of function values and gradients for triangular elements. Both the Poisson equation and the Laplace equation are discussed for polynomial finite element spaces (with degrees up to 8) under four different mesh patterns. Our results verify computer findings of Babuška et al., especially, we confirm that the computed data have 9 digits of accuracy with an exception of one pair (which has 8‐7 digits of accuracy). In addition, we demonstrate that the function value superconvergent points predicted by the symmetry theory of Schatz et al. are the only superconvergent points for the Poisson equation. Finally, we provide function value superconvergent points for the Laplace equation, which are not reported elsewhere in the literature. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.