Two-level finite element discretization of viscoelastic fluid flow Original Research Article

We propose and analyze a two-level method of discretizing the equations of steady-state flow of a viscoelastic fluid obeying an Oldroyd-type constitutive equation with no-slip boundary condition. The two-level algorithm consists of solving a small non-linear system of equations on the coarse mesh and then using that solution to solve a larger linear system on the fine mesh. Specifically, following Najib and Sandri [Numer. Math. 72 (1995) 223], we linearize the Oldroyd-type constitutive equation about the coarse mesh solution thus nullifying the difficulties brought by the advection term. Our theoretical error estimates show that it has optimal order accuracy provided the true solution is smooth and its norm is sufficiently small. In addition, our computational error estimates exhibit the validity of our analysis.