Approximation of time‐dependent, viscoelastic fluid flow: Crank‐Nicolson, finite element approximation

摘要: In this article we analyze a fully discrete approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation in ℝ, = 2, 3. We use Crank-Nicolson discretization for derivatives. At each level linear system of is solved. To resolve nonlinearities three-step extrapolation prediction velocity and stress at new level. The stabilized by using discontinuous Galerkin equation. For mesh parameter, h, temporal step size, Δt, sufficiently small satisfying Δt ≤ Ch, existence approximate solution proven. A priori error estimates terms h are also derived. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 248–283, 2004