We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler-Maruyama method. In both cases we obtain optimal error estimates. The proofs are based on sharp integral versions of well-known error estimates for the corresponding deterministic linear homogeneous equation together with optimal regularity results for the mild solution of the SPDE. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin approximations.
Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise
Galerkin finite element methods for the numerical solution of two classical-Boussinesq type systems over variable bottom topography
Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise
![QR code for arXiv:1103.4504 [math.NA]](http://oss.arxitics.com/images/favicon.svg)