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Natural and postprocessed superconvergence in semilinear problems
Author(s) -
Chow S.S.,
Carey G. F.,
Lazarov R. D.
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.1690070304
Subject(s) - superconvergence , mathematics , nonlinear system , derivative (finance) , operator (biology) , forcing (mathematics) , term (time) , mathematical analysis , finite element method , physics , repressor , thermodynamics , biochemistry , chemistry , quantum mechanics , gene , transcription factor , financial economics , economics
Abstract Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.