Analysis of discretization methods for nonlinear evolution equations
The mathematical modeling of time-dependent processes in science and engineering leads to in general nonlinear evolution equations of first or second order. The highest spatial derivatives appearing can often be described by a monotone and coercive operator; semilinearities are then treated as a strongly continuous perturbation of the principle part. Relying upon the variational approach and the theory of monotone operators, the numerical solution of such evolution problems is studied with a focus on time discretization methods on equidistant as well as non-uniform meshes and their convergence. The results apply in particular to fluid flow problems.