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Finite element solution of a stationary heat conduction equation with the radiation boundary condition. (English) Zbl 0782.65130
There exist many different methods of treating analytically and numerically the Stefan-Boltzmann boundary condition appearing in stationary heat conduction problems [e.g. T. Y. Na, Computational methods in engineering boundary value problems (1979; Zbl 0456.76002)]. Slightly modifying a variational approach briefly described by B. A. Szabó and I. Babuška [Finite element analysis, John Wiley & Sons, New York (1991)], the author examines here the associated finite element approximations.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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[1] Carrier G. F., Pearson C. E.: Partial differential equations. Theory and Technique, Academic Press, London, 1976. · Zbl 0323.35001
[2] Ciarlet P. G.: Optimisation, théorie et algorithmes. Dunod, Paris, 1971.
[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. · Zbl 0641.65092 · doi:10.1137/0724071
[4] Doktor P.: On the density of smooth functions in certain subspaces of Sobolev spaces. Comment. Math. Univ. Carolin. 14 (1973), 609-622. · Zbl 0268.46036 · eudml:16584
[5] Glowinski R.: Lectures on numerical methods for nonlinear variational problems. Tata Inst. of Fundamental Research, Bombay, 1980. · Zbl 0456.65035
[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. · Zbl 0754.73021 · eudml:15644
[8] Křížek M.: On semiregular families of triangulations und linear interpolation. Appl. Math. 36 (1991), 223-232. · Zbl 0728.41003 · eudml:15675
[9] 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.
[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. · Zbl 0145.36004
[14] Szabó B. A., Babuška I.: Finite element analysis. John Willey & Sons, New York, 1991. · Zbl 0792.73003
[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.
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