Solution of SPDEs with applications in porous media

Gabriel Lord, Heriot-Watt University

Abstract: We consider the numerical approximation of a general second order semi-linear parabolic stochastic partial differential equation (SPDE) driven by space-time noise. We introduce time-stepping schemes that use a linear functional of the noise and analyse a finite element discretization in space. We present convergence results and illustrate the work with examples motivated from realistic porous media flow.