Convergence analysis and numerical simulation for a hyperbolic system

In this paper, we develop and analyze a finite volume element method for the approximation of the hyperbolic type equations arising in mathematical physics in one space dimension. In recent years there has been increasing attention in the literatures to the development, analysis and implementation of the solution of hyperbolic equations. In this work, we construct the discrete finite volume element schemes, and give the optimal error estimates between the finite volume element solution and the exact solution. Moreover, numerical experiments are also provided to demonstrate the behavior of the methods and confirm the efficiency and robustness of the presented approach and method. Finally, some conclusions are obtained and our further research work is proposed.