  We consider a stochastic boundary value elliptic problem on a bounded domain
$D\subset \mathbb{R}^k$, driven by a fractional Brownian field with Hurst
parameter $H=(H_1,...,H_k)\in[{1/2},1[^k$. First we define the stochastic
convolution derived from the Green kernel and prove some properties. Using
monotonicity methods, we prove existence and uniqueness of solution, along with
regularity of the sample paths. Finally, we propose a sequence of lattice
approximations and prove its convergence to the solution of the SPDE at a given
rate.
