Voir la notice de l'article provenant de la source EDP Sciences
@article{MMNP_2009_4_1_a7, author = {V. Lleras}, title = {A {Stabilized} {Lagrange} {Multiplier} {Method} for the {Finite} {Element} {Approximation} of {Frictional} {Contact} {Problems} in {Elastostatics}}, journal = {Mathematical modelling of natural phenomena}, pages = {163--182}, publisher = {mathdoc}, volume = {4}, number = {1}, year = {2009}, doi = {10.1051/mmnp/20094108}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094108/} }
TY - JOUR AU - V. Lleras TI - A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics JO - Mathematical modelling of natural phenomena PY - 2009 SP - 163 EP - 182 VL - 4 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094108/ DO - 10.1051/mmnp/20094108 LA - en ID - MMNP_2009_4_1_a7 ER -
%0 Journal Article %A V. Lleras %T A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics %J Mathematical modelling of natural phenomena %D 2009 %P 163-182 %V 4 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094108/ %R 10.1051/mmnp/20094108 %G en %F MMNP_2009_4_1_a7
V. Lleras. A Stabilized Lagrange Multiplier Method for the Finite Element Approximation of Frictional Contact Problems in Elastostatics. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 163-182. doi : 10.1051/mmnp/20094108. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094108/
[1] R.A. Adams. Sobolev spaces, Academic Press, 1975.
[2] J. Mecan. Theor. Appl. 1988 67 82
,[3] Numer. Math. 1973 179 192
[4] Comput. Methods Appl. Mech. Engrg. 1991 109 128
,[5] Numer. Math. 1992 1 15
,[6] Comput. Methods Appl. Mech. Engrg. 1992 193 210
,[7] Math. Model. Numer. Anal. 2003 209 225
, ,[8] Math. Comp. 2003 83 104
,[9] SIAM J. Numer. Anal. 2005 1295 1320
, ,[10] Math. Comp. 2003 1117 1145
,[11] S.C. Brenner, L.R. Scott. The mathematical theory of finite element methods, Springer-Verlag, 2002.
[12] F. Brezzi. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, Rev. Franç. Automatique Inform. Rech. Opér., Sér. Rouge Anal. Numér., 8 (1974), 129–151.
[13] F. Brezzi, M. Fortin. Mixed and hybrid finite element methods, Springer, 1991.
[14] Numer. Math. 2001 641 659
[15] P.G. Ciarlet. The finite element method for elliptic problems, in Handbook of Numerical Analysis, eds. P.G. Ciarlet and J.L. Lions, North Holland, 2 (1991), 17–352.
[16] SIAM J. Numer. Anal. 2001 1324 1342
,[17] SIAM J. Sci. Comput. 2001 976 999
, ,[18] Math. Comp. 2002 1 25
, , ,[19] G. Duvaut. Problèmes unilatéraux en mécanique des milieux continus, in Actes du congrès international des mathématiciens (Nice 1970), Gauthier-Villars, 3 (1971), 71–77.
[20] G. Duvaut, J.L. Lions. Les inéquations en mécanique et en physique, Dunod, 1972.
[21] Math. Models Meth. Appl. Sci. 1998 445 468
,[22] C. Eck, J. Jarušek, M. Krbec. Unilateral contact problems: variational methods and existence theorems, Pure and Applied Mathematics, CRC Press, 270 (2005).
[23] W. Han, M. Sofonea. Quasistatic contact problems in viscoelasticity and viscoplasticity, American Mathematical Society, International Press, 2002.
[24] Numer. Math. 2005 91 115
, , ,[25] Math. Methods Appl. Sci. 1983 422 437
[26] J. Haslinger, I. Hlaváček, J. Nečas. Numerical methods for unilateral problems in solid mechanics, in Handbook of Numerical Analysis, Eds. P.G. Ciarlet and J.-L. Lions, North Holland, 4 (1996), 313–485.
[27] J. Haslinger, Y. Renard. A new fictitious domain approach inspired by the extended finite element method, submitted.
[28] Comput. Methods Appl. Mech. Engrg. 2003 4517 4531
, , ,[29] Comput. Methods Appl. Mech. Engrg. 2006 4323 4333
,[30] Q. Jl. Mech. Appl. Math. 2004 225 235
[31] Z. Angew. Math. Mech. 2005 673 680
[32] Appl. Numer. Math. 2002 401 421
,[33] SIAM J. Numer. Anal. 2007 2012 2031
,[34] P. Hild, Y. Renard. A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics, submitted.
[35] Czechoslovak. Math. J. 1983 237 261
[36] N. Kikuchi, J.T. Oden. Contact problems in elasticity : a study of variational inequalities and finite element methods, SIAM, 1988.
[37] D. Kinderlehrer, G. Stampacchia. An introduction to variational inequalities and their applications, Pure and Applied mathematics, Academic Press, New York-London, 1980.
[38] T. Laursen. Computational contact and impact mechanics, Springer, 2002.
[39] J.–L. Lions, E. Magenes. Problèmes aux limites non homogènes, Dunod, 1968.
[40] V. Lleras. Thesis, in preparation.
[41] V.G. Maz'ya, T.O. Shaposhnikova. Theory of multipliers in spaces of differentiable functions, Pitman, 1985.
[42] Int. J. Numer. Meth. Engng. 1999 131 150
, ,[43] Bolletino U. M. I. 1980 796 811
, ,[44] Abh. Math. Univ. Hamburg 1971 9 15
[45] Int. J. Num. Meth. Eng. 1992 1289 1309
,[46] SIAM J. Math. Anal. 2006 452 467
[47] M. Shillor, M. Sofonea, J.J. Telega. Models and analysis of quasistatic contact. Variational methods, Springer, 2004.
[48] J. Comput. Appl. Math. 1995 139 148
[49] P. Wriggers. Computational Contact Mechanics, Wiley, 2002.
Cité par Sources :