Finite Volume Element Method For Two Kinds Of Nonlinear Evolution Equations

The finite volume element method is a discretization technique for the par-tial differential equations,especially for those arising from physical conservation properties of the original problem locally,the finite volume element method has been widely used in computational fluid mechanics and heat transfer problems.In the past several decades,many researchers have studied this method extensively and obtained some important, results.In this paper,the object is to investigate the convergence of the finite volume element method of the two kinds of nonlinear evo-lution equations.In Chapter one,we summarize the background of the two kinds of nonlinear evolution equations.My job and The development of domestic and foreign for the two problem are also summarized.In Chapter two, the object is to investigate the convergence of the finite volume element method of the quasilinear hyperbolic equation We obtain optimal order error estimates for semi-discrete method and fully discrete method in L2-norm and H1-norm.In Chapter three, we consider discontinuous finite volume element method along characteristics for approximate the initial-boundary value problem of semi- conductor deviceThe method is a combination of characteristic method and discontinuous finite volume method.The new method not only inherits the advantages of discontinuous finite volume method, for example, high order accuracy, parallelizability and sim-plicity of space construction, it also possess some features of characteristic method: it is stable and can smear sharp fronts of the solution. By making the numerical analysis, We obtain optimal order error estimates for fully discrete method in H1 and suboptimal order error estimates for fully discrete method in L2.