Finite Element Approximation of the Linear Stochastic Wave Equation with Additive Noise

Semidiscrete finite element approximation of the linear stochastic wave equation with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies to multi-dimensional domains and spatially correlated noise. Numerical examples illustrate the theory. Key words. finite element method, stochastic wave equation, additive noise, Wiener process, stability, a priori error estimate, strong convergence AMS subject classifications. 65M60, 60H15, 60H35, 65C30

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Mihály Kovács, Stig Larsson, Fardin Saedpanah
• Keywords: Additive Noise, Error Estimate, SIAMNUM 2010, Stochastic Wave Equation