Finite volume method for solving the stochastic Helmholtz equation

• Main Authors: Ruimin Xu, Tingting Wu
• Format: Article
• Language: English
• Published: SpringerOpen 2019-03-01
• Series: Advances in Difference Equations
• Subjects: Stochastic Helmholtz equation; White noise; Finite volume method
• Online Access: http://link.springer.com/article/10.1186/s13662-019-2011-x

Abstract In this paper, we consider the linear finite volume method (FVM) for the stochastic Helmholtz equation, driven by white noise perturbed forcing terms in one-dimension. We first deduce the linear FVM for the deterministic Helmholtz problem. The dispersion equation is presented, and the error between the numerical wavenumber and the exact wavenumber is then analyzed. Comparisons between the linear FVM and the linear finite element method (FEM) are also made. The theoretical analysis and practical calculation indicate that the error of the linear FVM is half of that of the linear FEM. For the stochastic Helmholtz equation, convergence analysis and error estimates are given for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are provided to examine our theoretical results.