Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle

Maria I. M. Copetti

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 4, page 691-706
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Copetti, Maria I. M.. "Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.4 (2004): 691-706. <http://eudml.org/doc/244940>.

@article{Copetti2004,
abstract = {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.},
author = {Copetti, Maria I. M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thermoviscoelasticity; dynamic contact problem; finite element approximation; numerical simulations; hyperbolic-parabolic problem; existence; uniqueness},
language = {eng},
number = {4},
pages = {691-706},
publisher = {EDP-Sciences},
title = {Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle},
url = {http://eudml.org/doc/244940},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Copetti, Maria I. M.
TI - Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 4
SP - 691
EP - 706
AB - 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.
LA - eng
KW - thermoviscoelasticity; dynamic contact problem; finite element approximation; numerical simulations; hyperbolic-parabolic problem; existence; uniqueness
UR - http://eudml.org/doc/244940
ER -

References

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  1. [1] D.E. Carlson, Linear thermoelasticity, in Handbuch der physik, C. Truesdell Ed., VIa/2 (1972) 297–345. 
  2. [2] M.I.M. Copetti, A one-dimensional thermoelastic problem with unilateral constraint. Math. Comp. Simul. 59 (2002) 361–376. Zbl1011.74013
  3. [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. Zbl1130.74489
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  5. [5] C. Eck, Existence of solutions to a thermo-viscoelastic contact problem with Coulomb friction. Math. Mod. Meth. Appl. Sci. 12 (2002) 1491–1511. Zbl1173.74345
  6. [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. Zbl0949.74047
  7. [7] C.M. Elliott and T. Qi, A dynamic contact problem in thermoelasticity. Nonlinear Anal. 23 (1994) 883–898. Zbl0818.73061
  8. [8] S. Jiang and R. Racke, Evolution equations in thermoelasticity. Chapman & Hall/ CRC (2000). Zbl0968.35003MR1774100
  9. [9] J.U. Kim, A one-dimensional dynamic contact problem in linear viscoelasticity. Math. Meth. Appl. Sci. 13 (1990) 55–79. Zbl0703.73072
  10. [10] K.L. Kuttler and M. Shillor, A dynamic contact problem in one-dimensional thermoviscoelasticity. Nonlinear World 2 (1995) 355–385. Zbl0831.73054
  11. [11] M. Schatzman and M. Bercovier, Numerical approximation of a wave equation with unilateral constraints. Math. Comp. 53 (1989) 55–79. Zbl0683.65088

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