Finite element solutions for radiation cooling problems with nonlinear boundary conditions

 Access to full text

 Full (PDF)

1. [1] R. A. ADAMS, Sobolev SpacesSobolev Spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
2. [2] K. BABA and M. TABATA, On a conservative upwind finite element scheme forconvective diffusion equations, RAIRO Anal. Numér. 1515 (1981), 3-25. Zbl0466.76090MR610595
3. [3] P. G. CIARLET, Discrete maximum principle for finite-difference operators, Aequationes Math. 44 (1970), 338-352. Zbl0198.14601MR292317
4. [4] P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. Zbl0383.65058MR520174
5. [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. Zbl0251.65069MR375802
6. [6] D. S. COHEN, Generalized radiation cooling of a convex solid, J. Math. Anal. Appl. 35 (1971), 503-511. Zbl0218.35036MR284092
7. [7] A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, New Jersey, 1964. Zbl0144.34903MR181836
8. [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. Zbl0373.65047
9. [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. Zbl0469.65071MR619817
10. [10] K. ISHIHARA, Finite element approximations applied to the nonlinear boundary value problem $\Delta \left(u\right)=b{\left(u\right)}^2$, Publ. Res. Inst. Math. Sci. 18 (1982), 17-34. Zbl0492.65062MR660820
11. [11] K. ISHIHARA, Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem, Numer. Math. 43 (1984), 419-437. Zbl0531.65061MR738386
12. [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. Zbl0599.65074MR794607
13. [13] W. R. MANN and F. WOLF, Heat transfer between solids and gases under nonlinear boundary conditions, Quart. Appl. Math. 9 (1951), 163-184. Zbl0043.10001MR42596
14. [14] W. E. OLMSTEAD, Temperature distribution in a convex solid with nonlinear radiation boundary condition, J. Math. Mech. 15 (1966), 899-908. Zbl0145.36004MR197047
15. [15] J. M. ORTEGA, Numerical Analysis, Academic Press, New-York, 1972. Zbl0248.65001MR403154
16. [16] M. H. PROTTER and H. F. WEINBERGER, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1967. Zbl0153.13602MR219861
17. [17] R. E. SHOWALTER, Hilbert Space Methods for Partial Differential Equations, Pitman Press, London, 1977. Zbl0364.35001MR477394
18. [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. Zbl0151.15401MR192177
19. [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. Zbl0259.35020MR337023
20. [20] M. TABATA, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ. 18 (1978), 327-351. Zbl0391.65038MR495024
21. [21] V. THOMÉE, Polygonal domain approximation in Dirichlet's problem, J. Inst. Math. Appl. 11 (1973), 33-44. Zbl0246.35023MR349044
22. [22] R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. Zbl0133.08602MR158502