An augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity with piecewise linear equal-order finite elements

We study an augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity. The piecewise linear equal-order finite element spaces for both the velocity and the pressure approximations, proposed and analyzed by Latché and Vola [18], are applied. Based on the resulting regularity of the numerical solutions, a mesh adaptive strategy is proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme is formulated for general Herschel–Bulkley models, and its validity is verified on the benchmark model: Bingham fluid flows in a lid-driven square cavity.