Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt A9

Dynamics and asymptotic behaviour of stochastic evolution systems

13-056 Raphael Kruse.
Consistency and stability of a Milstein-Galerkin finite element scheme for semilinear SPDE

We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein- Galerkin finite element scheme. By a suitable generalization of the notion of bistability from Beyn & Kruse (DCDS B, 2010) to the semigroup framework in Hilbert spaces, our main result includes a two-sided error estimate of the spatio-temporal discretization. In an additional section we derive an analogous result for a Milstein-Galerkin finite element scheme with truncated noise.