Dissertation > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations

Coupling of Continous Fem and the Robust Discontinuous Galerkin Method for Convction Diffusion Equations

Author HeJingWei
Tutor ZhangHongWei
School Changsha University of Science and Technology
Course Computational Mathematics
Keywords Convection-diffusion problem Continuous Finite Element Method Discontinuous Finite Element Method Coupling method
CLC O241.82
Type Master's thesis
Year 2011
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In recent years, the numerical solution of singularly perturbed boundary value problem has been widespread concern, but the continuous finite element method in dealing with complex boundary problem has its own deficiencies and shortcomings , but discontinuous finite element method to maintain the finite element method (FEM) and finite volume method (FVM) advantages , but also overcome its shortcomings , particularly easy to deal with complex boundary issues . 2001 , I.Perugia and D.Scho tzau on the use of the advantages of both a coupled approach to solving such problems. Since then, the coupling method has been continuously developed . The main work is continuous and discontinuous finite element method combined with the finite element method to solve a class of singularly perturbed convection-diffusion equation . Its main contents are as follows: The first chapter introduces some discontinuous finite element and finite element historical background , research trends and major problems . Chapter II of this chapter is a constant coefficient equations are convection-diffusion equation , through the selection of a special numerical traces to prove the stability of coupling method . Chapter III for a class of unsteady convection-diffusion equation by the interval into two disjoint subintervals at different intervals using different methods, and by selecting a special numerical track , we analyzed show that the coupling method is stable. Chapter coupling method for the error analysis of the method is given . Chapter V through numerical experiments , we verify the feasibility of the method .

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