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Superconvergence of recovered gradients of discrete time/piecewise linear Galerkin approximations for linear and nonlinear parabolic problems
Author(s) -
Wheeler Mary F.,
Whiteman J. R.
Publication year - 1994
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.1690100303
Subject(s) - superconvergence , mathematics , piecewise linear function , galerkin method , context (archaeology) , piecewise , nonlinear system , space (punctuation) , mathematical analysis , finite element method , discontinuous galerkin method , parabolic partial differential equation , partial differential equation , paleontology , linguistics , philosophy , physics , quantum mechanics , biology , thermodynamics
Superconvergent error estimates in l 2 ( H 1 ) and l ∞( H 1 ) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc.