A weighted least-squares finite element method for Phan-Thien-Tanner viscoelastic fluid

In this paper, we present the weighted least-squares finite element approximations to the steady Phan-Thien-Tanner (PTT) viscoelastic fluid. We approximate the nonlinear viscoelastic model by linearizing the constitutive equation and apply a least-squares method to solve the linearized system. The least-squares functional involves the residuals of each equation in L2-norm multiplied by mesh dependent weights. The method is tested on a planar channel flow problem. Numerical results exhibit the convergence rates of the proposed scheme.