A Stochastic Galerkin Method for Stochastic Control Problems (Communications in Computational Physics, 2014)
In an interdisciplinary field on mathematics and physics, we examine aphysical problem, fluid flow in porous media, which is represented by a stochasticpartial differential equation (SPDE). We first give a priori error estimates for the solutions to an optimization problem constrained by the physical model under lowerregularity assumptions than the literature. We then use the concept of Galerkin finite element methods to establish a new numerical algorithm to give approximationsfor our stochastic optimal physical problem. Finally, we develop original computerprograms based on the algorithm and use several numerical examples of various situations to see how well our solver works by comparing its outputs to the priori errorestimates.