Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion models
Abstract
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank--Nicolson finite difference formulation. In the stochastic direction, we also employ a random variable based on the Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.
Keywords
Cite
@article{arxiv.1904.06263,
title = {Analysis of a Legendre spectral element method (LSEM) for the two-dimensional system of a nonlinear stochastic advection-reaction-diffusion models},
author = {Mostafa Abbaszadeh and Amirreza Khodadadian and Mehdi Dehghan and Thomas Wick},
journal= {arXiv preprint arXiv:1904.06263},
year = {2019}
}