Mixed finite element approximation for the stochastic pressure equation of Wick type

We propose a mixed finite element method for the numerical solution of the stochastic pressure equation of Wick type. In this formulation, the pressure and the velocity are the most relevant unknowns. We give existence and uniqueness results for the continuous problem and its approximation. Optimal error estimates are derived and algorithmic aspects are discussed. Finally, the results of numerical experiments confirm the practical efficiency of the mixed method.