Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 691-706.

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.

DOI : 10.1051/m2an:2004029
Classification : 65N30
Mots-clés : thermoviscoelasticity, dynamic contact problem, finite element approximation, numerical simulations 
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     title = {Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Copetti, Maria I. M. Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 691-706. doi : 10.1051/m2an:2004029. http://www.numdam.org/articles/10.1051/m2an:2004029/

[1] D.E. Carlson, Linear thermoelasticity, in Handbuch der physik, C. Truesdell Ed., VIa/2 (1972) 297-345.

[2] M.I.M. Copetti, A one-dimensional thermoelastic problem with unilateral constraint. Math. Comp. Simul. 59 (2002) 361-376. | Zbl

[3] M.I.M. Copetti and D.A. French, Numerical solution of a thermoviscoelastic contact problem by a penalty method. SIAM J. Numer. Anal. 41 (2003) 1487-1504. | Zbl

[4] W.A. Day, Heat conduction with linear thermoelasticity. Springer, New York (1985). | MR | Zbl

[5] C. Eck, Existence of solutions to a thermo-viscoelastic contact problem with Coulomb friction. Math. Mod. Meth. Appl. Sci. 12 (2002) 1491-1511.

[6] C. Eck and J. Jaruček, The solvability of a coupled thermoviscoelastic contact problem with small Coulomb friction and linearized growth of frictional heat. Math. Meth. Appl. Sci. 22 (1999) 1221-1234. | Zbl

[7] C.M. Elliott and T. Qi, A dynamic contact problem in thermoelasticity. Nonlinear Anal. 23 (1994) 883-898. | Zbl

[8] S. Jiang and R. Racke, Evolution equations in thermoelasticity. Chapman & Hall/ CRC (2000). | MR | Zbl

[9] J.U. Kim, A one-dimensional dynamic contact problem in linear viscoelasticity. Math. Meth. Appl. Sci. 13 (1990) 55-79. | Zbl

[10] K.L. Kuttler and M. Shillor, A dynamic contact problem in one-dimensional thermoviscoelasticity. Nonlinear World 2 (1995) 355-385. | Zbl

[11] M. Schatzman and M. Bercovier, Numerical approximation of a wave equation with unilateral constraints. Math. Comp. 53 (1989) 55-79. | Zbl

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