Etienne Emmrich
Technische Universität Berlin

Analysis of time discretisation methods for nonlinear evolution problems
Many time-depending problems in science and engineering can be described by the initial-value problem for a nonlinear evolution equation of first or second order. In this talk, we present new results on the convergence of the temporal semi-discretisation by several standard methods on uniform and non-uniform time grids.

The evolution equation under consideration is assumed to be governed by a time-depending operator that is coercive, monotone, and fulfills a certain growth and continuity condition. Strongly continuous perturbations are also studied.

By employing algebraic relations, which reflect the stability of the numerical method, and based upon the theory of monotone operators, the convergence of piecewise polynomial prolongations of the time discrete solutions towards a weak solution is shown. The analysis does not require any additional regularity of the exact solution. The results apply to several fluid flow problems such as incompressible non-Newtonian shear-thickening fluid flow.