Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
Magenes, E. ; Nochetto, R. H. ; Verdi, C.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987), p. 655-678 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1987__21_4_655_0,
     author = {Magenes, Enrico and Nochetto, R. H. and Verdi, C.},
     title = {Energy error estimates for a linear scheme to approximate nonlinear parabolic problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {21},
     year = {1987},
     pages = {655-678},
     mrnumber = {921832},
     zbl = {0635.65123},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1987__21_4_655_0}
}

Magenes, E.; Nochetto, R. H.; Verdi, C. Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987) pp. 655-678. http://gdmltest.u-ga.fr/item/M2AN_1987__21_4_655_0/

[1] Ph. Benilan, Solutions intégrales d'équations d'évolution dans un espace de Banach, C. R. Acad. Sci. Paris, A-274 (1972), 47-50. | MR 300164 | Zbl 0246.47068

[2] A. E. Berger, H Brezis & J. C. W. Rogers, A numerical method for solving the problem u t -Δf(u)=0 R.A.I.R.O. Anal. Numér., 13 (1979), 297-312. | Numdam | MR 555381 | Zbl 0426.65052

[3] A. Bossavit, A. Damlamian & M. Fremond Eds., Free boundary problems: applications and theory, vol. III, Research Notes in Math. 120, Pitman, Boston (1985). | MR 863154 | Zbl 0578.35003

[4] H. Brezis, On some degenerate non-linear parabolic equations, in Non-linear functional analysis (F. E. Browder Ed.), A.M.S. XVIII 1 (1970), 28-38. | MR 273468 | Zbl 0231.47034

[5] H. Brezis & A. Pazy, Convergence and approximation of semigroups of non-linear operators in Banach spaces, J. Funct. Anal., 9 (1972), 63-74. | MR 293452 | Zbl 0231.47036

[6] J. F. Ciavaldini, Analyse numérique d'un problème de Stefan à deux phases par une méthode d'éléments finis, SIAM J. Numer. Anal., 12 (1975), 464-487. | MR 391741 | Zbl 0272.65101

[7] M. G. Crandall & T. M. Liggett, Generation of semi-groups of non-linear transformations on general Banach spaces, Amer J. Math., 93 (1971), 265-298. | MR 287357 | Zbl 0226.47038

[8] J. Douglas Jr. & T. Dupont, Galerkin methods for parabolic equations, SIAM J. Numer. Anal., 7 (1970), 575-626. | MR 277126 | Zbl 0224.35048

[9] J. Douglas Jr. & T. Dupont, Alternating-direction Galerkin methods on rectangles, in Numerical solutions of partial differential equations, vol. II (B. Hubbard Ed.), Academic Press, New York (1971), 133-214. | MR 273830 | Zbl 0239.65088

[10] J. Douglas Jr., T. Dupont & R. E. Ewing, Incomplete iteration for time-stepping a Galerkin method for a quasilinear parabolic problem, SIAM J. Numer. Anal., 16 (1979), 503-522. | MR 530483 | Zbl 0411.65064

[11] C. M. Elliott, Error analysis of the enthalpy method for the Stefan problem, IMA J. Numer. Anal., 7 (1987), 61-71. | MR 967835 | Zbl 0638.65088

[12] R. E. Ewing, Efficient multistep procedures for nonlinear parabolic problems with nonlinear Neumann boundary conditions, Calcolo, 19 (1982), 231-252. | MR 695388 | Zbl 0522.65072

[13] J. W. Jerome, Approximation of nonlinear evolution systems, Academic Press, New York (1983). | MR 690582 | Zbl 0512.35001

[14] J. W. Jerome & M. E. Rose, Error estimates for the multidimensional two-phase Stefan problem, Math. Comp., 39 (1982), 377-414. | MR 669635 | Zbl 0505.65060

[15] J. L. Lions & E. Magenes, Non-homogeneous boundary value problems and applications, vol. I, Springer-Verlag, Berlin (1972). | MR 350177 | Zbl 0223.35039

[16] M. Luskin, A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions, SIAM J. Numer. AnaL, 16 (1979), 284-299. | MR 526490 | Zbl 0405.65059

[17] E. Magenes, Problemi di Stefan bifase in piu variabili spaziali, V S.A.F.A., Catania, Le Matematiche, XXXVI (1981), 65-108. | Zbl 0545.35096

[18] E. Magenes & C. Verdi, On the semigroup approach to the two-phase Stefan problem with nonlinear flux conditions, in [3], 28-39. | MR 863159 | Zbl 0593.35092

[19] G. H. Meyer, Multidimensional Stefan problems, SIAM J. Numer. Anal., 10 (1973), 522-538. | MR 331807 | Zbl 0256.65054

[20] R. H. Nochetto, Error estimates for two-phase Stefan problems in several space variables, I: linear boundary conditions, Calcolo, 22 (1985), 457-499. | MR 859087 | Zbl 0606.65084

[21] R. H. Nochetto, Error estimates for two-phase Stefan problems in several space variables, II: nonlinear flux conditions, Calcolo, 22 (1985), 501-534. | MR 859088 | Zbl 0606.65085

[22] R. H. Nochetto, Error estimates for multidimensional Stefan problems with general boundary conditions, in [3], 50-60. | MR 863161 | Zbl 0593.35094

[23] R. H. Nochetto, Error estimates for multidimensional singular parabolic problems, Japan J. Appl. Math., 4 (1987), 111-138. | MR 899207 | Zbl 0657.65132

[24] R. H. Nochetto & C. Verdi, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., to appear. | MR 954786 | Zbl 0655.65131

[25] J. C. W. Rogers, A. E. Berger & M. Ciment, The alternating phase truncation method for numerical solution of a Stefan problem, SIAM J. Numer. Anal., 16 (1979), 563-587. | MR 537272 | Zbl 0418.65051

[26] M. E. Rose, Numerical methods for flows through porous media I, Math. Comp., 40 (1983), 435-467. | MR 689465 | Zbl 0518.76078

[27] V. Thomee, Galerkin finite element methods for parabolic problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin (1984). | MR 744045 | Zbl 0528.65052

[28] C. Verdi, On the numerical approach to a two-phase Stefan problem with nonlinear flux, Calcolo, 22 (1985), 351-381. | MR 860658 | Zbl 0612.65084

[29] C. Verdi & A. Visintin, Error estimates for a semi-explicit numerical scheme for Stefan-type problems, submitted to Numer. Math. | MR 923709 | Zbl 0617.65125

[30] A. Visintin, Stefan problem with phase relaxation, IMA J. Appl. Math., 34 (1985), 225-245. | MR 804824 | Zbl 0585.35053

[31] M. F. Wheeler, A priori L 2 -error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal., 10 (1973), 723-759. | MR 351124 | Zbl 0232.35060

[32] R. E. White, An enthalpy formulation of the Stefan problem, SIAM J. Numer. Anal., 19 (1982), 1129-1157. | MR 679656 | Zbl 0501.65058