  In this paper, we present finite element approximations of a class of
Generalized random fields defined over a bounded domain of R d or a smooth
d-dimensional Riemannian manifold (d $\ge$ 1). An explicit expression for the
covariance matrix of the weights of the finite element representation of these
fields is provided and an analysis of the approximation error is carried out.
Finally, a method to generate simulations of these weights while limiting
computational and storage costs is presented.
