GLS and EVSS methods for a three-field Stokes problem arising from viscoelastic flows Original Research Article

In this paper, order one finite elements together with Galerkin least-squares (GLS) methods are used for solving a three-field Stokes problem arising from the numerical study of viscoelastic flows. Stability and convergence results are established, even when the solvent viscosity is small compared to the viscosity due to the polymer chains. An iterative algorithm decoupling velocity–pressure and stress calculations is proposed. The link with the modified elastic viscous split stress (EVSS) method studied in (M. Fortin, R. Guénette, R. Pierre, Comput. Methods Appl. Mech. Engrg. 143 (1997) 79–95; R. Guénette, M. Fortin, J. Non-Newtonian Fluid Mech. 60 (1995) 27–52) is presented. Numerical results are in agreement with theoretical predictions, and with those presented in (M. Fortin, R. Guénette, R. Pierre, Comput. Methods Appl. Mech. Engrg. 143 (1997) 79–95).