An Modified Nonlinear Galerkin Method For The Viscoelastic Fluid Motion Equations

In this article we first provide a priori estimates of the solution for the nonstationary two-dimensional viscoelastic fluid motion equations with periodic boundary condition. We then present an modified nonlinear Galerkin method for solving such equations. By comparing the convergence rates of the proposed method with the standard Galerkin method, we conclude that the modified nonlinear Galerkin method is better than the standard Galerkin method because the former can save a large amount of computational work and maintain the convergence rate of the latter. 1. Introduction In this paper we consider Oldroyd's mathematical model of two-dimensional viscoelastic fluid motion. Such model ( see [1] ) can be defined by the rheological relation k 0 oe + k 1 @oe @t = j 0 ¸ + j 1 @¸ @t ; k 1 oe(0; x) = j 1 ¸(0; x); (1.1) where oe is the stress tensor and ¸ is the strain tensor, and k 0 ; k 1 ; j 0 ; j 1 are positive constants. In fact ¸ = (¸ i;j ) is the 2 \Theta 2 matrix with components ..