no. 3
Finite element solutions for radiation cooling problems with nonlinear boundary conditions
ESAIM: Modélisation mathématique et analyse numérique, Tome 20 (1986) no. 3, pp. 461-477. 
@article{M2AN_1986__20_3_461_0,
     author = {Ishihara, Kazuo},
     title = {Finite element solutions for radiation cooling problems with nonlinear boundary conditions},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {461--477},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {20},
     number = {3},
     year = {1986},
     mrnumber = {862787},
     zbl = {0618.65100},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1986__20_3_461_0/}
}
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Ishihara, Kazuo. Finite element solutions for radiation cooling problems with nonlinear boundary conditions. ESAIM: Modélisation mathématique et analyse numérique, Tome 20 (1986) no. 3, pp. 461-477. http://www.numdam.org/item/M2AN_1986__20_3_461_0/

[1] R. A. Adams, Sobolev SpacesSobolev Spaces, Academic Press, New York, 1975. | MR | Zbl

[2] K. Baba and M. Tabata, On a conservative upwind finite element scheme forconvective diffusion equations, RAIRO Anal. Numér. 1515 (1981), 3-25. | Numdam | MR | Zbl

[3] P. G. Ciarlet, Discrete maximum principle for finite-difference operators, Aequationes Math. 44 (1970), 338-352. | MR | Zbl

[4] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. | MR | Zbl

[5] P. G. Ciarlet and P. A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17-31. | MR | Zbl

[6] D. S. Cohen, Generalized radiation cooling of a convex solid, J. Math. Anal. Appl. 35 (1971), 503-511. | MR | Zbl

[7] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, New Jersey, 1964. | MR | Zbl

[8] H. Fujii, Some remarks on finite element analysis of time-dependent field problems, Theory and Practice in Finite Element Structural Analysis (ed. by Yamada, and Gallagher, R. H.), 91-106, Univ. of Tokyo Press, Tokyo, 1973. | Zbl

[9] K.On Finite Element Schemes Of The Dirichlet Problem For A System Of Ishihara, On finite element schemes of the Dirichlet problem for a system of nonlinear elliptic equations, Numer. Funct. Anal. Optim. 3 (1981), 105-136. | MR | Zbl

[10] K. Ishihara, Finite element approximations applied to the nonlinear boundary value problem Δ(u)=b(u) 2 , Publ. Res. Inst. Math. Sci. 18 (1982), 17-34. | MR | Zbl

[11] K. Ishihara, Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem, Numer. Math. 43 (1984), 419-437. | MR | Zbl

[12] K. Ishihara, Explicit iterations with monotonicity for finite element approximations applied to a system of nonlinear elliptic equations, J. Approx. Theory 44 (1985), 241-252. | MR | Zbl

[13] W. R. Mann and F. Wolf, Heat transfer between solids and gases under nonlinear boundary conditions, Quart. Appl. Math. 9 (1951), 163-184. | MR | Zbl

[14] W. E. Olmstead, Temperature distribution in a convex solid with nonlinear radiation boundary condition, J. Math. Mech. 15 (1966), 899-908. | MR | Zbl

[15] J. M. Ortega, Numerical Analysis, Academic Press, New-York, 1972. | MR | Zbl

[16] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1967. | MR | Zbl

[17] R. E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman Press, London, 1977. | MR | Zbl

[18] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965), 189-258. | Numdam | MR | Zbl

[19] G. Strang and A. Berger, The change in solution due to change in domain, Proc. Sympos. Pure Math. on Partial Differential Equations, 23 (1973), 199-205. | MR | Zbl

[20] M. Tabata, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ. 18 (1978), 327-351. | MR | Zbl

[21] V. Thomée, Polygonal domain approximation in Dirichlet's problem, J. Inst. Math. Appl. 11 (1973), 33-44. | MR | Zbl

[22] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. | MR | Zbl