Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations
Journal article, 1998

We consider semidiscrete solutions in quasi-uniform finite element spaces of order O(hr) 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 R^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.

Author

A. H. Schatz

Vidar Thomee

University of Gothenburg

Department of Mathematics

L. B. Wahlbin

Communications on Pure and Applied Mathematics

0010-3640 (ISSN) 1097-0312 (eISSN)

Vol. 51 11-12 1349-1385

Subject Categories

Computational Mathematics

Roots

Basic sciences

DOI

10.1002/(SICI)1097-0312(199811/12)51

More information

Created

10/8/2017