A Multigrid Method for Viscoelastic Fluid Flow

Abstract

We study a multigrid finite element method for a viscoelastic fluid flow obeying an Oldroyd-B--type constitutive law. The multigrid method is a time-saving method in which the full nonlinear system is solved on a coarse grid, and subsequent approximations are generated on a succession of refined grids by solving a linearized problem. We show that the linearized problem has an approximate solution and present an error bound for a two-grid method. We also numerically demonstrate that the multigrid method is significantly more efficient than the standard one-grid finite element method.