A combined BDF‐semismooth Newton approach for time‐dependent Bingham flow |
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| Authors: | J C De Los Reyes S González Andrade |
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| Institution: | 1. Research Group on Optimization, Departamento de Matemática, Escuela Politécnica Nacional Quito, Ecuador and Institut für Mathematik, Humboldt‐Universit?t zu Berlin, Germany;2. Research Group on Optimization, Departamento de Matemática, Escuela Politécnica Nacional Quito, Ecuador and Institut für Mathematik und Wissenschaftliches Rechnen, University of Graz, Graz, Austria |
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| Abstract: | 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 |
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| Keywords: | backward differentiation methods Bingham fluids parabolic variational inequalities semismooth Newton methods Tikhonov regularization |
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