We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher). © 2010 Elsevier B.V. All rights reserved.
- Galerkin method
- Numerical solution of stochastic PDEs
- Pathwise convergence
- Stochastic exponential integrator