M. Geissert, M. Kovacs, and S. Larsson

Rate of weak convergence of the finite element method
for the stochastic heat equation with additive noise,

preprint 2008:8, Department of Mathematical Sciences, 
Chalmers University of Technology
BIT 2009, to appear 

Abstract

The stochastic heat equation driven by additive noise is discretized
in the spatial variables by a standard finite element method.  The
weak convergence of the approximate solution is investigated and the
rate of weak convergence is found to be twice that of strong
convergence.