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

2011/03/10 by Gabriel J. Lord, Lord, Gabriel J, Antoine Tambue +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1103.1986

openalex publication_date 2011/03/10 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We consider the numerical approximation of a general second order\nsemi--linear parabolic stochastic partial differential equation (SPDEs) driven\nby space-time noise, for multiplicative and additive noise. We examine\nconvergence of exponential integrators for multiplicative and additive noise.\nWe consider noise that is in trace class and give a convergence proof in the\nmean square L² norm. We discretize in space with the finite element method\nand in our implementation we examine both the finite element and the finite\nvolume methods. We present results for a linear reaction diffusion equation in\ntwo dimensions as well as a nonlinear example of two-dimensional stochastic\nadvection diffusion reaction equation motivated from realistic porous media\nflow.\n

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• Optimal Error Estimates of a Finite Element Method for Semilinear SPDEs with Additive Noise and Nonsmooth Initial Data
• Easy-to-Implement One-Step Schemes for Stochastic Integration
• Exponential Runge-Kutta Galerkin finite element method for a reaction-diffusion system with nonsmooth initial data

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