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Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations
Author(s) -
Schatz A. H.,
Thomée V.,
Wahlbin L. B.
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199811/12)51:11/12<1349::aid-cpa5>3.0.co;2-1
Subject(s) - mathematics , bounded function , analytic semigroup , norm (philosophy) , mathematical analysis , semigroup , logarithm , boundary value problem , domain (mathematical analysis) , neumann boundary condition , political science , law
We consider semidiscrete solutions in quasi‐uniform finite element spaces of order O ( h r ) of the initial boundary value problem with Neumann boundary conditions for a second‐order parabolic differential equation with time‐independent coefficients in a bounded domain in $Ropf: N . We show that the semigroup on L ∞ , defined by the semidiscrete solution of the homogeneous equation, is bounded and analytic uniformly in h . We also show that the semidiscrete solution of the inhomogeneous equation is bounded in the space‐time L ∞ ‐norm, modulo a logarithmic factor for r = 2, and we give a corresponding almost best approximation property. © 1998 John Wiley & Sons, Inc.