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.
