Chen, Zhiming; Nochetto, Ricardo H.; Schmidt, Alfred
Error control and adaptivity for a phase relaxation model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 4 , p. 775-797
Zbl 0965.65114 | MR 1784485 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=M2AN_2000__34_4_775_0

Bibliographie

[1] Z. Chen and R.H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527-548. MR 1742264 | Zbl 0943.65075

[2] Z. Chen, R.H. Nochetto and A. Schmidt, Adaptive finite element methods for diffuse interface models (in preparation).

[3] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). MR 520174 | Zbl 0383.65058

[4] Ph. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. Numdam | MR 400739 | Zbl 0368.65008

[5] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. I. A linear model problem. SIAM J. Numer. Anal. 28 (1991) 43-77. MR 1083324 | Zbl 0732.65093

[6] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. IV. Nonlinear problems. SIAM J. Numer. Anal. 32 (1995) 1729-1749. MR 1360457 | Zbl 0835.65116

[7] K. Eriksson, C. Johnson and S. Larsson, Adaptive finite element methods for parabolic problems. VI. Analytic semigroups. SIAM J. Numer. Anal 35 (1998) 1315-1325. MR 1620144 | Zbl 0909.65063

[8] P. Grisvard, Elliptic Problems on Non-smooth Domains. Pitman, Boston (1985). Zbl 0695.35060

[9] X. Jiang and R.H. Nochetto, Optimal error estimates for semidiscrete phase relaxation models. RAIRO Model. Math. Anal. Numér. 31 (1997) 91-120. Numdam | MR 1432853 | Zbl 0874.65069

[10] X. Jiang and R.H. Nochetto, A P1 - P1 finite element method for a phase relaxation model. I. Quasi uniform mesh. SIAM J. Numer. Anal. 35 (1998) 1176-1190. MR 1619875 | Zbl 0972.65067

[11] X. Jiang, R.H. Nochetto and C. Verdi, A Pl - P1 finite element method for a phase relaxation model. II. Adaptively refined meshes. SIAM J. Numér. Anal. 36 (1999) 974-999. MR 1688994 | Zbl 0934.65105

[12] R.H. Nochetto, M. Paolini and C. Verdi, Continuous and semidiscrete traveling waves for a phase relaxation model. European J. Appl. Math. 5 (1994) 177-199. MR 1285038 | Zbl 0812.35166

[13] R.H. Nochetto, G. Savaré and C. Verdi, Error control for nonlinear evolution equations. C.R. Acad. Sci. Paris Sér. I 326 (1998) 1437-1442. MR 1649189 | Zbl 0944.65077

[14] R.H. Nochetto, G. Savaré and C. Verdi, A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. 53 (2000) 529-589. MR 1737503 | Zbl 1021.65047

[15] R.H. Nochetto, A. Schmidt and C. Verdi, A posteriori error estimation and adaptivity for degenerate parabolic problems. Math. Comp. 69 (2000) 1-24. MR 1648399 | Zbl 0942.65111

[16] C. Verdi and A. Visintin, Numerical analysis of the multidimensional Stefan problem with supercooling and superheating. Boll. Un. Mat. Ital. B 7 (1987) 795-814. MR 916294 | Zbl 0629.65130

[17] C. Verdi and A. Visintin, Error estimates for a semi-explicit numerical scheme for Stefan-type problems. Numer. Math. 52 (1988) 165-185. MR 923709 | Zbl 0617.65125

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

[19] A. Visintin, Supercooling and superheating effects in phase transitions. IMA J. Appl. Math. 35 (1986) 233-256. MR 839201 | Zbl 0615.35090