Semi-discretization of stochastic partial differential equations on Rd by a finite-element technique

This paper discusses some finite-element schemes for the approximation of the solution of stochastic partial differential equations on Rd. The main application is the design of approximate filters in the general case of correlated noise. The need to interpolate the solution with functions of compact support requires to estimate its norm in a suitable weighted Sobolev space. It turns out that it is possible to control the mean square of the error norm with a suitable modification near the boundary of the most used finite-elements triangulations