Eskil Hansen: Splitting based integrators for dissipative evolution equations

The aim of this talk is to give an overview of some recent progress when analyzing splitting schemes applied to nonlinear parabolic problems. Such equations are frequently encountered in biology, chemistry and physics, as they e.g. describe reaction-diffusion systems. More precisely, we will consider splitting based integrators for evolution equations governed by m-dissipative vector fields. The dissipative property yields a rather general framework which serves as the foundation of our numerical analysis. First, we recapitulate some of the classical approximation results by Brezis and Pazy, which yield convergence of several splitting schemes. Secondly, we present a new strategy for deriving convergence orders for a family of (formally) first-order schemes when, e.g., applied to degenerate parabolic equations with delay source terms and the abstract Riccati equation.