On solving elliptic stochastic partial differential equations
A model elliptic boundary value problem of second order, with stochastic coefficients described by the KarhunenLove expansion is addressed. This problem is transformed into an equivalent deterministic one. The perturbation method and the method of successive approximations is analyzed. Rigorous error estimates in the framework of Sobolev spaces are given.
stochastic partial differential equations karhunenlove expansion successive approximations numerical solution of partial differential equations