2010/04/12 by Gabriel J. Lord, Lord, Gabriel J, Antoine Tambue +1
Decision Sciences · Engineering · #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods in engineering #Pattern Formation and Solitons (nlin.PS) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.1004.1998
openalex publication_date 2010/04/12 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28
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 a linear functional of the noise with a semi--implicit Euler--Maruyama method in time and in space we analyse a finite element method (although extension to finite differences or finite volumes would be possible). We prove convergence in the root mean square L2 norm for a diffusion reaction equation and diffusion advection reaction equation. 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 see from both the analysis and numerics that the proposed scheme has better convergence properties than the standard semi--implicit Euler--Maruyama method.