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Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
Author(s) -
Wheeler M. F.,
Whiteman J. R.
Publication year - 1987
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.1690030407
Subject(s) - superconvergence , mathematics , finite element method , piecewise linear function , piecewise , gravitational singularity , boundary value problem , element (criminal law) , boundary (topology) , order (exchange) , mathematical analysis , structural engineering , finance , political science , law , engineering , economics
Engineers have been aware for some time of the phenomenon of superconvergence, whereby there exist (stress) points at which the accuracy of a finite‐element solution is superior to that of the approximation generally. This phenomenon has been treated in recent years by mathematicians who have proved, for certain two‐dimensional second‐order elliptic problems, superconvergent error estimates for retrieved finite‐element derivatives. These results have demanded high global regularity of the solutions of the boundary value problems. In this present article cut‐off functions are used to prove similar superconvergence results over interior subdomains. This allows superconvergence estimates to be derived for problems with solutions of low global regularity, particularly those involving singularities.