Numerical Analysis of Semilinear Parabolic Problems

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.