Article
Full entry |
PDF
(1.1 MB)
Feedback
PDF
(1.1 MB)
Feedback
Keywords:
heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction
heat conduction; heat radiation; finite elements; Stefan-Boltzmann boundary condition; stationary heat conduction
Summary:
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.
References:
[1] Carrier G. F., Pearson C. E.: Partial differential equations. Theory and Technique, Academic Press, London, 1976. MR 0404823 | Zbl 0323.35001
[2] Ciarlet P. G.: Optimisation, théorie et algorithmes. Dunod, Paris, 1971. MR 0298892
[3] Delfour M. C., Payre G., Zolésio J. P.: Approximation of nonlinear problems associated with radiating bodies in the space. SIAM J. Numer. Anal. 24 (1987), 1077-1094. DOI 10.1137/0724071 | MR 0909066
[4] Doktor P.: On the density of smooth functions in certain subspaces of Sobolev spaces. Comment. Math. Univ. Carolin. 14 (1973), 609-622. MR 0336317
[5] Glowinski R.: Lectures on numerical methods for nonlinear variational problems. Tata Inst. of Fundamental Research, Bombay, 1980. MR 0597520
[6] Hottel A. C., Sarofim A.F.: Radiative transport. McGraw Hill, New York, 1965.
[7] Jarušek J.: On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. Apl. Math 35 (1990), 426-450. MR 1089924
[8] Křížek M.: On semiregular families of triangulations und linear interpolation. Appl. Math. 36 (1991), 223-232. MR 1109126
[8] Křížek M., Neitaanmaki P.: Finite element approximation of variational problems and applications. Longam, Harlow, 1990.
[10] Na T. Y.: Computational methods in engineering boundary value problems. Academic Press, London, 1979, pp. 231,232,279. Zbl 0456.76002
[11] Nečas J.: Les méthodes directes en théorie des eqations elliptiques. Academia, Prague, 1967. MR 0227584
[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.
[13] Olmstead W. E.: Temperature distribution in a convex solid with a nonlinera radiation boundary condition. J. Math. Mech. 15 (1966), 899-907. MR 0197047
[14] Szabó B. A., Babuška I.: Finite element analysis. John Willey & Sons, New York, 1991. MR 1164869
[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.
[16] Vujanovič B., Strauss A. M.: Heat transfer with nonlinear boundary conditions via a variational principle. AIAA (1971), 327-330.
Search
Partner of
