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Maximum‐norm superapproximation of the gradient for the trilinear block finite element
Author(s) -
Liu Jinghong,
Zhu Qiding
Publication year - 2007
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.20237
Subject(s) - mathematics , superconvergence , norm (philosophy) , finite element method , boundary value problem , partial derivative , block (permutation group theory) , mathematical analysis , partial differential equation , boundary values , geometry , physics , political science , law , thermodynamics
For a model elliptic boundary value problem in three dimensions, we give the weak estimate of the first type for trilinear block elements and the estimate for W 1,1 ‐seminorm of the discrete derivative Green's function over rectangular partitions of the domain, from which we obtain maximum‐norm superapproximation of the gradient for the trilinear block finite element approximation. Furthermore, utilizing this superapproximation, we can also obtain maximum‐norm superconvergence of the gradient. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007