Semidiscrete Galerkin approximation for a linear stochastic parabolic partial differential equation driven by an additive noise
We study the semidiscrete Galerkin approximation of a stochastic parabolic partial differential equation forced by an additive space-time noise. The discretization in space is done by a piecewise linear finite element method. The space-time noise is approximated by using the generalized L-2 projection operator. Optimal strong convergence error estimates in the L-2 and (H) over dot(-1) norms with respect to the spatial variable are obtained. The proof is based on appropriate nonsmooth data error estimates for the corresponding deterministic parabolic problem. The error estimates are applicable in the multi-dimensional case.
stochastic parabolic partial differential equations additive noise finite element method hilbert space