Numerical analysis of semilinear parabolic problems

Stig Larsson

Lectures delivered at the EPSRC VIII-th Summer School in
Numerical Analysis, University of Leicester, July 12--17, 1998.

Published in  
``The Graduate Student's Guide to Numerical Analysis '98'', 
editors M. Ainsworth, J. Levesley, and M. Marletta, 
SSCM volume 26, Springer-Verlag, 1999, pp. 83-117.

Department of Mathematics,
Chalmers University of Technology and G\"oteborg University,
SE--412 96 G\"oteborg,
Sweden

e-mail: stig@math.chalmers.se 
URL:    http://www.math.chalmers.se/~stig

Abstract:

  In these lectures I discuss error analysis techniques for finite
  element methods for systems of reaction-diffusion equations with
  applications in dynamical systems theory.  The emphasis is on
  pedagogical aspects and analysis techniques rather than on results.
  The list of techniques discussed include: analytic semigroup,
  parabolic smoothing, non-smooth data error estimate, a priori error
  estimate, a posteriori error estimate, exponential dichotomy,
  shadowing.