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

Maria I.M. Copetti

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 38.4 (2010): 691-706. <http://eudml.org/doc/194234>.

@article{Copetti2010,
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},
keywords = {Thermoviscoelasticity; dynamic contact problem; finite element approximation; numerical simulations.; hyperbolic-parabolic problem; existence; uniqueness},
language = {eng},
month = {3},
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/194234},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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/194234
ER -

References

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  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.  Zbl1011.74013
  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
  4. W.A. Day, Heat conduction with linear thermoelasticity. Springer, New York (1985).  Zbl0577.73009
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  6. C. Eck and J. Jarušek, 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. C.M. Elliott and T. Qi, A dynamic contact problem in thermoelasticity. Nonlinear Anal.23 (1994) 883–898.  Zbl0818.73061
  8. S. Jiang and R. Racke, Evolution equations in thermoelasticity. Chapman & Hall/ CRC (2000).  Zbl0968.35003
  9. J.U. Kim, A one-dimensional dynamic contact problem in linear viscoelasticity. Math. Meth. Appl. Sci.13 (1990) 55–79.  Zbl0703.73072
  10. K.L. Kuttler and M. Shillor, A dynamic contact problem in one-dimensional thermoviscoelasticity. Nonlinear World2 (1995) 355–385.  Zbl0831.73054
  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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