Numerical approximation of the Oldroyd-B model by the weighted least-squares/discontinuous Galerkin method



We consider a numerical method for the Oldroyd-B model of viscoelastic fluid flows by a combination of the weighted least-squares (WLS) method and the discontinuous Galerkin (DG) finite element method. The constitutive equation is decoupled from the momentum and continuity equations, and the approximate solution is computed iteratively by solving the Stokes problem and a linearized constitutive equation using WLS and DG, respectively. An a priori error estimate for the WLS/DG method is derived and numerical results supporting the estimate are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013