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

作者：De Los Reyes J C^*; Andrade S Gonzalez

来源：Numerical Methods for Partial Differential Equations, 2012, 28(3): 834-860.

DOI：10.1002/num.20658

• backward differentiation methods
• Bingham fluids
• parabolic variational inequalities
• semismooth Newton methods
• Tikhonov regularization

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.

• 出版日期2012-5