In this article we first provide a priori estimates of the solution for the
nonstationary two-dimensional viscoelastic fluid motion equations with per
iodic boundary condition. We then present an modified nonlinear Galerkin me
thod for solving such equations. By comparing the convergence rates of the
proposed method with the standard Galerkin method, we conclude that the mod
ified nonlinear Galerkin method is better than the standard Galerkin method
because the former can save a large amount of computational work and maint
ain the convergence rate of the latter. (C) 1999 Elsevier Science Ltd. All
rights reserved.