Research Of Mixed Finite Method And Convergence Properties Of Oldroyd B Type Fluid Flow

R.Courant firstly presented the finite element method in 1943. Professor K. Feng and western scientists respectively structured the mathematical theory of finite element methods. At present, mixed finite element method, least-square mixed finite element method, multi-scale mixed finite element method and multi-grid method have been generally applied in many industry and solved many really problems. In this paper, our essential work is to solve viscoelastic fluid flow obeying an Oldroyd B type constitutive law by apply the mixed finite element method, least-square mixed finite element method and V-cycle multi-grid method.In the first chapter, we mainly introduce the background and the status of recent researches of the finite element method.In the second chapter, we study the mixed finite element method of Oldroyd B type viscoelastic fluid flow model, and we give the existence and uniqueness of approximation solution and error bounded.In the third chapter, by applying the least-square mixed finite element method to study Oldroyd B type viscoelastic fluid flow model, we discuss the existence and uniqueness of approximation solution and convergence.In the fourth chapter, we analysis the V-cycle multi-grid formulation of Oldroyd B type viscoelastic fluid flow model, and we give the existence and uniqueness of iterative solution and error estimates.