A sign preserving mixed finite element approximation for contact problems
By: Patrick Hild
Open Access
|Sep 2011References
- Adams, R. (1975)., Academic Press, New York, NY/London.
- Belhachmi, Z., Sac-EpéeAe, J.-M. and Sokolowski, J. (2005). Mixed finite element methods for smooth domain formulation of crack problems,43(3): 1295-1320.
- Ben Belgacem, F. and Brenner, S. (2001). Some nonstandard finite element estimates with applications to 3D Poisson and Signorini problems,12: 134-148.
- Ben Belgacem, F., Hild, P. and Laborde, P. (1999). Extension of the mortar finite element method to a variational inequality modeling unilateral contact,9(2): 287-303.
- Ben Belgacem, F. and Renard, Y. (2003). Hybrid finite element methods for the Signorini problem,72(243): 1117-1145.
- Bernardi, C. and Girault, V. (1998). A local regularisation operator for triangular and quadrilateral finite elements,35(5): 1893-1916.
- Brenner, S. and Scott, L. (2002)., Springer-Verlag, New York, NY.
- Chen, Z. and Nochetto, R. (2000). Residual type a posteriori error estimates for elliptic obstacle problems,84(4): 527-548.
- Ciarlet, P. (1991). The finite element method for elliptic problems,P.G. Ciarlet and J.-L. Lions (Eds.),, Vol. II, Part 1, North Holland, Amsterdam, pp. 17-352.
- CléeAment, P. (1975). Approximation by finite element functions using local regularization,2(R-2): 77-84.
- Coorevits, P., Hild, P., Lhalouani, K. and Sassi, T. (2002). Mixed finite element methods for unilateral problems: Convergence analysis and numerical studies,71(237): 1-25.
- Duvaut, G. and Lions, J.-L. (1972)., Paris.
- Eck, C., Jarušek, J. and Krbec, M. (2005)., CRC Press, Boca Raton, FL.
- Fichera, G. (1964). Elastic problems with unilateral constraints, the problem of ambiguous boundary conditions,8(7): 91-140, (in Italian).
- Fichera, G. (1974). Existence theorems in linear and semilinear elasticity,54(12): 24-36.
- Grisvard, P. (1985)., Pitman, Boston, MA.
- Han, W. and Sofonea, M. (2002)., American Mathematical Society, Providence, RI.
- Haslinger, J., HlavéaAček, I. and Nečas, J. (1996). Numerical methods for unilateral problems in solid mechanics,P. Ciarlet and J.-L. Lions (Eds.),, Vol. IV, Part 2, North Holland, Amsterdam, pp. 313-485.
- Hilbert, S. (1973). A mollifier useful for approximations in Sobolev spaces and some applications to approximating solutions of differential equations,27: 81-89.
- Hild, P. (2000). Numerical implementation of two nonconforming finite element methods for unilateral contact,184(1): 99-123.
- Hild, P. (2002). On finite element uniqueness studies for Coulomb's frictional contact model,12(1): 41-50.
- Hild, P. and Nicaise, S. (2007). Residual a posteriori error estimators for contact problems in elasticity,41(5): 897-923.
- Hiriart-Urruty, J.-B. and LemaréeAchal, C. (1993)., Springer, Berlin.
- HéuUeber, S. and Wohlmuth, B. (2005a). An optimal error estimate for nonlinear contact problems,43(1): 156-173.
- HéuUeber, S. and Wohlmuth, B. (2005b). A primal-dual active set strategy for non-linear multibody contact problems,194(27-29): 3147-3166.
- Khludnev, A. and Sokolowski, J. (2004). Smooth domain method for crack problems,62(3): 401-422.
- Kikuchi, N. and Oden, J. (1988)., SIAM, Philadelphia, PA.
- Laursen, T. (2002)., Springer, Berlin.
- Nochetto, R. and Wahlbin, L. (2002). Positivity preserving finite element approximation,71(240): 1405-1419.
- Scott, L. and Zhang, S. (1990). Finite element interpolation of nonsmooth functions satisfying boundary conditions,54(190): 483-493.
- Strang, G. (1972). Approximation in the finite element method,19: 81-98.
- Wohlmuth, B. and Krause, R. (2003). Monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems,25(1): 324-347.
- Wriggers, P. (2002)., Wiley, Chichester.
Language: English
Page range: 487 - 498
Published on: Sep 22, 2011
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Related subjects:
© 2011 Patrick Hild, published by University of Zielona Góra
This work is licensed under the Creative Commons License.