STABILITY, ANALYTICITY, AND ALMOST BEST APPROXIMATION IN MAXIMUM NORMFOR PARABOLIC FINITE-ELEMENT EQUATIONS

We consider semidiscrete solutions in quasi-uniform finite element spa ces of order O(h(r)) of the initial boundary value problem with Neuman n boundary conditions for a second-order parabolic differential equati on with time-independent coefficients in a bounded domain in R-N. We s how that the semigroup on L-infinity, defined by the semidiscrete solu tion of the homogeneous equation, is bounded and analytic uniformly in h. We also show that the semidiscrete solution of the inhomogeneous e quation is bounded in the space-time L-infinity-norm, module a logarit hmic factor for r = 2, and we give a corresponding almost best approxi mation property. (C) 1998 John Wiley & Sons, Inc.