A combined BDF‐semismooth Newton approach for time‐dependent Bingham flow

This article is devoted to the numerical simulation of time‐dependent convective Bingham flow in cavities. Motivated by a primal‐dual regularization of the stationary model, a family of regularized time‐dependent problems is introduced. Well posedness of the regularized problems is proved, and convergence of the regularized solutions to a solution of the original multiplier system is verified. For the numerical solution of each regularized multiplier system, a fully discrete approach is studied. A stable finite element approximation in space together with a second‐order backward differentiation formula for the time discretization are proposed. The discretization scheme yields a system of Newton differentiable nonlinear equations in each time step, for which a semismooth Newton algorithm is used. We present two numerical experiments to verify the main properties of the proposed approach. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011