Finite Volume Element Methods For High-order Wave Equations And Seawater Intrusion Problerm

The contents of this dissertation are divided into two chapters.Chapter one studied a fully-discrete finite volume element methods for high-order wave equations.For the time term, we use central difference methods to discrete; for the space term,we use finite volume element methods to discrete. In the paper, the existence and the convergence of the fully-discrete scheme are proved. Some numerical results are also presented.Chapter two studied up-wind finite volume element, method for the seawater intrusion problem.The seawater intrusion problem is modeled as coupled two parabolic differential equation, of which one is a flow equation for the pressure , the other one a convection-diffusion equation for the density. In this paper, we set up a finite volume element method to approximate the seawater intrusion model. To the convection item, we treat with up-wind method. H~1 norm error estimates are got.