Coupling Of Continous Fem And The Robust Discontinuous Galerkin Method For Convction Diffusion Equations

In recent years, more and more people pay attention to the numericalsolutions of singularly perturbed boundary value problems. However, thecontinuous finite element methods can't solve the convection diffusionproblems complex boundary value problems, but the discontinuous Galerkinmethods have the good properties of FEM and FVM, and overcome it's badproperties. Moreover it goods at to deal with complex boundary valueproblems. . In 2001, I.Perugia and D.scho&&tzau used the coupling method tosolve problems. Successively, the coupling method develop further.In this paper, our essential work is to solve the singularly perturbedconvection diffusion equations by using the coupling method of thecontinuous finite method and the discontinuous Galerkin method. The maincontents as follows:In the first chapter, we mainly introduce the background and the statusof recent researches of the finite element method and discontinuousGalerkin method, and the main problem which we discuss.In the second chapter, we provide the special example of the secondchapter which the coefficient is a constant. We also prove the stability ofthe method.In the third chapter, we mainly study the equation which the coefficientis a function. Dividing the region into two disjoint regions, in differentregions we use different methods, and choose some special number traces,in the end we provide the stability of the method.In the fouth chapter, we give the error analysis of the coupling method.In the last chapter, we present the numerical example to demonstratethe feasibility of our method.