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A priori error estimation of \(hp\)-finite element approximations of frictional contact problems with normal compliance. (English) Zbl 0772.73078

Summary: An analysis of a class of contact problems with friction characterized by interfaces obeying a normal compliance law is given. A priori error estimations are developed for general cases and for the special case in which only steady sliding occurs. These estimates are applicable to \(h\)-, \(p\)- and \(hp\)-finite element approximations and give estimated rates of convergence for general \(hp\)-methods. A regularization of the friction law transforms variational inequalities corresponding to the general problem of contact with friction into nonlinear equations which can be solved by standard methods. A priori error estimations are also developed for these regularized problems. Numerical examples are given to support the theoretical results.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
65N06 Finite difference methods for boundary value problems involving PDEs
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[1] Oden, J. T.; Martins, J. A.C., Comput. Meth. Appl. Mech. Engng, 52, 527-634 (1985)
[2] Martins, J. A.C., (Ph.D. Dissertation (1985), Univ. Of Texas: Univ. Of Texas Austin, Tex)
[3] Kikuchi, N.; Oden, J. T., Contact Problems in Elasticity (1988), SIAM: SIAM Philadelphia · Zbl 0685.73002
[4] Rabier, P.; Martins, J. A.C.; Oden, J. T.; Campos, L., Int. J. Engng Sci., 24, 1755-1768 (1986)
[5] Klarbring, A.; Mikelic, A.; Shiller, M., Nonlinear Anal. Theory Meth. Applic., 13, 935-955 (1989)
[6] Adams, R. A., Sobolev Spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101
[7] Demkowicz, L.; Oden, J. T., Nonlinear Anal. Theory Meth. Applic., 6, 1075-1093 (1982)
[8] Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O., Comput. Meth. Appl. Mech. Engng, 77, 79-112 (1989)
[9] Oden, J. T.; Demkowicz, L.; Rachowicz, W.; Westermann, T. A., Comput. Meth. Appl. Mech. Engng, 77, 113-180 (1989)
[10] Rachowicz, W.; Oden, J. T.; Demkowicz, L., Comput. Meth. Appl. Mech. Engng, 77, 181-212 (1989)
[11] J. T. ODEN, Preprint.; J. T. ODEN, Preprint.
[12] Babuška, I.; Suri, M., Math. Modell. Numer. Anal., 21, 199-238 (1987)
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