Research Of Convergence Peoperties Two-grid Methods Of Oldroyd B Type Fluid Flow

Oldroyd B type viscoelastic fluid belong to the scope of the non-Newtonian fluid, is to solve complex fluid dynamics classic and one of the famous model. Between fluid and solid, so the variable with complex constitutive relations. Oldroyd-B fluid model has always been a hot issue of the finite element analysis.The main work is viscoelastic fluid problem for a class of obedience Oldroyd-B fluid differential, the use of mixed finite element and two networks on solving regional split, to prove the existence and uniqueness of the finite element approximation solution. This paper is divided into three chapters, structured as follows:In the first chapter,we mainly introduces the research background, the topics in accordance with the innovative work of research and papers.the second chapter is devoted to the numerical analysis of a stabilized finite element approximation for viscoelastic fluid flow obeying an Oldroyd B type constitutice law.The approximate stress,velocity and ptessure are repectively Pk discontinuous, Pk+i continuous and Pk continuous for an arbitrary integer k>0.When assuming the continuous problem is proved tu have a unique solution by employing a fixed point method,and an error estimate is derived.In the third chapter, does not contain a relatively simple form of twisted tensor Oldroyd-B fluid flow problems by mixed finite element and two to be consistent triangulation network for solving the region, and the establishment of coarse and fine grid. First, in the fine grid iterative elimination portion of the residual projection operator, and then use the residual amount is transferred to the coarse grid, and finally further correction on the coarse grid. By constructing finite element discretization scheme to prove that such a two-grid algorithm finite element approximation Convergence of Solutions and error analysis.