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Superconvergence of recovered gradients of piecewise quadratic finite element approximations. Part I: L 2 ‐error estimates
Author(s) -
Goodsell G.,
Whiteman J. R.
Publication year - 1991
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.1690070106
Subject(s) - superconvergence , mathematics , finite element method , quadratic equation , piecewise , norm (philosophy) , piecewise linear function , elasticity (physics) , element (criminal law) , approximations of π , mathematical analysis , linear elasticity , geometry , physics , materials science , political science , law , composite material , thermodynamics
Superconvergence properties in the L 2 norm are derived for the recovered gradients of piecewise quadratic finite element approximations on triangular partitions for two‐dimensional elliptic problems and systems, including the case of linear elasticity. The analysis covers problems defined on polygonal domains, where the solutions have low regularity. The effects of numerical integration are treated.