Paper Info
Title
A modified semi-implicit Euler-Maruyama scheme for finite element discretization of SPDEs with additive noise.
Abstract
We consider the numerical approximation of a general second order semi–linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new modified scheme using linear functionals of the noise with the semi–implicit Euler–Maruyama method in time, and the finite element method in space (although extension to finite differences or finite volumes would be possible). We prove the convergence in the root mean square L2 norm for a diffusion reaction equation and diffusion advection reaction equation with a large family of Lipschitz nonlinear functions. We present numerical results for a linear reaction diffusion equation in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We observe from both the analysis and numerics that the proposed scheme has better convergence properties than the standard semi–implicit Euler–Maruyama method.
Year
DOI
Venue
2018
10.1016/j.amc.2018.03.014
Applied Mathematics and Computation
Keywords
Field
DocType
Parabolic stochastic partial differential equations,Finite element method,modified semi–implicit Euler–Maruyama,Higher order approximation,Strong numerical approximation,Additive noise,Transport in porous media.
Mathematical optimization,Mathematical analysis,FTCS scheme,Finite element method,Numerical solution of the convection–diffusion equation,Stochastic partial differential equation,Partial differential equation,Mathematics,Diffusion equation,Finite volume method for one-dimensional steady state diffusion,Mixed finite element method
Journal
Volume
ISSN
Citations 
332
0096-3003
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Gabriel J. Lord13312.31
Antoine Tambue282.72