We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itô chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordina...

We use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Moreover, the latte...