The Mortar finite element method for Bingham fluids

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1. [1] Y. Achdou and O. Pironneau, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite elements and boundary element methods. SIAM J. Numer. Anal. 32 (1995) 985–1016. Zbl0833.76032
2. [2] R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). Zbl0314.46030MR450957
3. [3] F. Ben Belgacem, The mixed mortar finite element method for the incompressible Stokes problem: Convergence analysis. SIAM J. Numer. Anal. 37 (2000) 1085–1100. Zbl0959.65126
4. [4] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. Zbl0944.65114
5. [5] F. Ben Belgacem, P. Hild and P. Laborde, Extension of the mortar finite element method to a variational inequality modeling unilateral contact. Math. Models Methods Appl. Sci. 9 (1999) 287–303. Zbl0940.74056
6. [6] C. Bernardi, N. Debit and Y. Maday, Coupling finite element and spectral methods: First results. Math. Comp. 54 (1990) 21–39. Zbl0685.65098
7. [7] C. Bernardi and V. Girault, A Local regularisation operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35 (1998) 1893–1916. Zbl0913.65007
8. [8] C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar, H. Brezis and J.–L. Lions Eds., Pitman (1994) 13–51. Zbl0797.65094
9. [9] P.E. Bjørstad and O.B. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23 (1986) 1097–1120. Zbl0615.65113
10. [10] H. Brezis, Monotonicity in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to nonlinear functional analysis, E. Zarantonello Ed., Academic Press, New York (1971) 101-156. Zbl0278.47033MR394323
11. [11] P.–G. Ciarlet, The finite element method for elliptic problems, in Handbook of numerical analysis, Vol. II, Part 1, P.–G. Ciarlet and J.–L. Lions Eds., North Holland, Amsterdam (1991) 17–352. Zbl0875.65086
12. [12] N. Debit, La méthode des éléments avec joints dans le cas du couplage de méthodes spectrales et méthodes d’éléments finis: résolution des équations de Navier-Stokes. Ph.D. thesis, University of Paris VI, France (1991). 
13. [13] G. Duvaut and J.–L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972). Zbl0298.73001
14. [14] R.S. Falk, Error estimates for the approximation of a class of variational inequalities. Math. Comp. 28 (1974) 963–971. Zbl0297.65061
15. [15] R. Glowinski, Lectures on numerical methods for non–linear variational problems. Springer, Berlin (1980). Zbl0456.65035
16. [16] P. Hild, Problèmes de contact unilatéral et maillages éléments finis incompatibles. Ph.D. thesis, University of Toulouse III, France (1998). 
17. [17] J.–L. Lions and G. Stampacchia, Variational inequalities. Comm. Pure. Appl. Math. XX (1967) 493–519. Zbl0152.34601
18. [18] P.P. Mosolov and V.P. Miasnikov, Variational methods in the theory of the fluidity of a viscous-plastic medium. PPM, J. Mech. Appl. Math. 29 (1965) 545–577. Zbl0168.45505
19. [19] P.P. Mosolov and V.P. Miasnikov, On stagnant flow regions of a viscous-plastic medium in pipes. PPM, J. Mech. Appl. Math. 30 (1966) 841–854. Zbl0168.45601
20. [20] P.P. Mosolov and V.P. Miasnikov, On qualitative singularities of the flow of a viscoplastic medium in pipes. PPM, J. Mech Appl. Math. 31 (1967) 609–613. Zbl0236.76006