Stochastic exponential integrators for finite element discretization of SPDEs for multiplicative and additive noise

Details Stochastic exponential integrators for finite element discretization of SPDEs for multiplicative and additive noise Stochastic exponential integrators for finite element discretization of SPDEs for multiplicative and additive noise

2011-03-10

arxiv.org/abs/1103.1986v2

Mathematics

Numerical Analysis

Scientific paper

We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDEs) driven by space-time noise, for multiplicative and additive noise. We examine convergence of exponential integrators for multiplicative and additive noise. We consider noise that is in trace class and give a convergence proof in the 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 two-dimensional stochastic advection diffusion reaction equation motivated from realistic porous media flow.

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