Free Access
Volume 43, Number 1, January-February 2009
Page(s) 81 - 117
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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you