Finite element solution of a stationary heat conduction equation with the radiation boundary condition

Zdeněk Milka

Applications of Mathematics (1993)

  • Volume: 38, Issue: 1, page 67-79
  • ISSN: 0862-7940

Abstract

top
In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space H 1 ( Ω ) are examined.

How to cite

top

Milka, Zdeněk. "Finite element solution of a stationary heat conduction equation with the radiation boundary condition." Applications of Mathematics 38.1 (1993): 67-79. <http://eudml.org/doc/15737>.

@article{Milka1993,
abstract = {In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space $H^1 (\Omega )$ are examined.},
author = {Milka, Zdeněk},
journal = {Applications of Mathematics},
keywords = {heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction; Stefan-Boltzmann boundary condition; stationary heat conduction; finite element},
language = {eng},
number = {1},
pages = {67-79},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element solution of a stationary heat conduction equation with the radiation boundary condition},
url = {http://eudml.org/doc/15737},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Milka, Zdeněk
TI - Finite element solution of a stationary heat conduction equation with the radiation boundary condition
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 1
SP - 67
EP - 79
AB - In this paper we present a weak formulation of a two-dimensional stationary heat conduction problem with the radiation boundary condition. The problem can be described by an operator which is monotone on the convex set of admissible functions. The relation between classical and weak solutions as well as the convergence of the finite element method to the weak solution in the norm of the Sobolev space $H^1 (\Omega )$ are examined.
LA - eng
KW - heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction; Stefan-Boltzmann boundary condition; stationary heat conduction; finite element
UR - http://eudml.org/doc/15737
ER -

References

top
  1. Carrier G. F., Pearson C. E., Partial differential equations, Theory and Technique, Academic Press, London, 1976. (1976) Zbl0323.35001MR0404823
  2. Ciarlet P. G., Optimisation, théorie et algorithmes, Dunod, Paris, 1971. (1971) MR0298892
  3. Delfour M. C., Payre G., Zolésio J. P., 10.1137/0724071, SIAM J. Numer. Anal. 24 (1987), 1077-1094. (1987) MR0909066DOI10.1137/0724071
  4. Doktor P., On the density of smooth functions in certain subspaces of Sobolev spaces, Comment. Math. Univ. Carolin. 14 (1973), 609-622. (1973) MR0336317
  5. Glowinski R., Lectures on numerical methods for nonlinear variational problems, Tata Inst. of Fundamental Research, Bombay, 1980. (1980) MR0597520
  6. Hottel A. C., Sarofim A.F., Radiative transport, McGraw Hill, New York, 1965. (1965) 
  7. Jarušek J., On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes, Apl. Math 35 (1990), 426-450. (1990) MR1089924
  8. Křížek M., On semiregular families of triangulations und linear interpolation, Appl. Math. 36 (1991), 223-232. (1991) MR1109126
  9. Křížek M., Neitaanmaki P., Finite element approximation of variational problems and applications, Longam, Harlow, 1990. (1990) 
  10. Na T. Y., Computational methods in engineering boundary value problems, Academic Press, London, 1979, pp. 231,232,279. (1979) Zbl0456.76002
  11. Nečas J., Les méthodes directes en théorie des eqations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  12. Ohayon R., Gorge Y., Variational analysis of a non-linear non-homogenous heat conduction problem, Proc. Conf. Numerical Methods for Non-linar Problems, Swansea 1980, Pineridge Press, pp. 673-681. (1980) 
  13. Olmstead W. E., Temperature distribution in a convex solid with a nonlinera radiation boundary condition, J. Math. Mech. 15 (1966), 899-907. (1966) MR0197047
  14. Szabó B. A., Babuška I., Finite element analysis, John Willey & Sons, New York, 1991. (1991) MR1164869
  15. Vujanovič B., Djukič. D., On the variational principle of Hamilton's typr for nonlinear heat transfer problem, Internat. J. Heat. Mass Transfer (1972), 1111-1123. (1972) 
  16. Vujanovič B., Strauss A. M., Heat transfer with nonlinear boundary conditions via a variational principle, AIAA (1971), 327-330. (1971) 

NotesEmbed ?

top

You must be logged in to post comments.