Maximum-norm estimates for parabolic finite element equations

Vidar Thomee

Department of Mathematics
Chalmers University of Technology and
The University of G\"oteborg
Sweden
 


Abstract:  We consider spatially semidiscrete and fully discrete
finite element approximations
of the solution of  an initial-boundary value problem for
a parabolic equation. We survey known results concerning
stability and error estimates with respect to the
maximum-norm, including some recent developments.
The presentation relates to
properties of analytic semigroups and their approximation.