We consider the numerical approximation of a general second-order semilinear parabolic stochastic partial differential equation driven by multiplicative and additive space-time noise. We examine convergence of exponential integrators for multiplicative and additive noise. We consider noise that is in a trace class and give a convergence proof in the root-mean-square L-2 norm. We discretize in space with the finite element method and in our implementation we examine both the finite element and the finite volume methods. We present results for a linear reaction-diffusion equation in two dimensions as well as a nonlinear example of a two-dimensional stochastic advection-diffusion-reaction equation motivated from realistic porous media flow.
- parabolic stochastic partial differential equation
- finite element
- exponential integrators
- strong numerical approximation
- multiplicative noise
- additive noise