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Pointwise supercloseness of tensor‐product block finite elements
Author(s) -
Liu Jinghong,
Zhu Qiding
Publication year - 2009
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.20384
Subject(s) - mathematics , pointwise , tensor product , projection (relational algebra) , mathematical analysis , finite element method , interpolation (computer graphics) , partial derivative , pure mathematics , norm (philosophy) , function (biology) , algorithm , image (mathematics) , physics , artificial intelligence , computer science , political science , law , thermodynamics , evolutionary biology , biology
In this article, we first introduce interpolation operator of projection type in three dimensions, from which we then derive weak estimates for tensor‐product block finite elements of degree m ≥ 1. Finally, using estimates for the discrete Green's function and the discrete derivative Green's function, we prove that both of the gradient and the function value of the finite element solution u h and the corresponding interpolant Π m u of projection type and degree m are superclose in the pointwise sense of the L ∞ ‐norm. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009