Work

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

Year: 2012

Type: article

Abstract: 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 L2 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.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/drr059

Authors: G. J. Lord, A. Tambue

Institutions: Heriot-Watt University, Maxwell Institute for Mathematical Sciences

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W2151860842

FWCI: 6.181

Cites: 24

Cited by: 100

Related to: 20