Free Access
Issue
ESAIM: M2AN
Volume 43, Number 1, January-February 2009
Page(s) 81 - 117
DOI https://doi.org/10.1051/m2an/2008039
Published online 16 October 2008
  1. J. Alberty, C. Carstensen and S. Funken, Remarks around 50 lines of Matlab: short finite element implementation. Numer. Algorithms 20 (1999) 117–137. [Google Scholar]
  2. H.W. Alt, Lineare Funktionalanalysis. Springer-Verlag (1999). [Google Scholar]
  3. A. Bensoussan and J. Frehse, Regularity Results for Nonlinear Elliptic Systems and Applications, Applied Mathematical Sciences 151. Springer-Verlag (2002). [Google Scholar]
  4. H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to Non-linear Functional Analysis, E. Zarantonello Ed., Acad. Press (1971) 101–156. [Google Scholar]
  5. J.C. De Los Reyes and K. Kunisch, A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations. Nonlinear Anal. 62 (2005) 1289–1316. [CrossRef] [MathSciNet] [Google Scholar]
  6. E.J. Dean, R. Glowinski and G. Guidoboni, On the numerical simulation of Bingham visco-plastic flow: Old and new results. J. Non-Newtonian Fluid Mech. 142 (2007) 36–62. [Google Scholar]
  7. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics. Springer-Verlag, Berlin (1976). [Google Scholar]
  8. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland Publishing Company, The Netherlands (1976). [Google Scholar]
  9. M. Fuchs and G. Seregin, Some remarks on non-Newtonian fluids including nonconvex perturbations of the Bingham and Powell-Eyring model for viscoplastic fluids. Math. Models Methods Appl. Sci. 7 (1997) 405–433. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Fuchs and G. Seregin, Regularity results for the quasi-static Bingham variational inequality in dimensions two and three. Math. Z. 227 (1998) 525–541. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Fuchs, J.F. Grotowski and J. Reuling, On variational models for quasi-static Bingham fluids. Math. Methods Appl. Sci. 19 (1996) 991–1015. [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics. Springer-Verlag (1984). [Google Scholar]
  13. R. Glowinski, J.L. Lions and R. Tremolieres, Analyse numérique des inéquations variationnelles. Applications aux phénomènes stationnaires et d'évolution 2, Méthodes Mathématiques de l'Informatique, No. 2. Dunod (1976). [Google Scholar]
  14. M. Hintermüller and K. Kunisch, Path-following methods for a class of constrained minimization problems in function spaces. SIAM J. Optim. 17 (2006) 159–187. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Hintermüller and K. Kunisch, Feasible and non-interior path-following in constrained minimization with low multiplier regularity. SIAM J. Contr. Opt. 45 (2006) 1198–1221. [Google Scholar]
  16. M. Hintermüller and G. Stadler, An infeasible primal-dual algorithm for TV-based inf-convolution-type image restoration. SIAM J. Sci. Comput. 28 (2006) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semi-smooth Newton method. SIAM J. Optim. 13 (2003) 865–888. [CrossRef] [MathSciNet] [Google Scholar]
  18. R.R. Huilgol and Z. You, Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel-Bulkley fluids. J. Non-Newtonian Fluid Mech. 128 (2005) 126–143. [CrossRef] [Google Scholar]
  19. K. Ito and K. Kunisch, Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces. Nonlinear Anal. 41 (2000) 591–616. [CrossRef] [MathSciNet] [Google Scholar]
  20. K. Ito and K. Kunisch, Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: M2AN 37 (2003) 41–62. [CrossRef] [EDP Sciences] [Google Scholar]
  21. J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag (1971). [Google Scholar]
  22. P.P. Mosolov and V.P. Miasnikov, Variational methods in the theory of the fluidity of a viscous-plastic medium. J. Appl. Math. Mech. (P.M.M.) 29 (1965) 468–492. [Google Scholar]
  23. T. Papanastasiou, Flows of materials with yield. J. Rheology 31 (1987) 385–404. [CrossRef] [Google Scholar]
  24. G. Stadler, Infinite-dimensional Semi-smooth Newton and Augmented Lagrangian Methods for Friction and Contact Problems in Elasticity. Ph.D. thesis, Karl-Franzens University of Graz, Graz, Austria (2004). [Google Scholar]
  25. G. Stadler, Path-following and augmented Lagrangian methods for contact problems in linear elasticity. J. Comp. Appl. Math. 203 (2007) 533–547. [CrossRef] [Google Scholar]
  26. D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM J. Optim. 7 (1997) 463–480. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Ulbrich, Nonsmooth Newton-like methods for variational inequalities and constrained optimization problems in function spaces. Habilitation thesis, Technische Universität München, Germany (2001–2002). [Google Scholar]

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