Error control and adaptivity for a phase relaxation model

Zhiming Chen; Ricardo H. Nochetto; Alfred Schmidt

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 4, page 775-797
  • ISSN: 0764-583X

How to cite

top

Chen, Zhiming, Nochetto, Ricardo H., and Schmidt, Alfred. "Error control and adaptivity for a phase relaxation model." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.4 (2000): 775-797. <http://eudml.org/doc/194012>.

@article{Chen2000,
author = {Chen, Zhiming, Nochetto, Ricardo H., Schmidt, Alfred},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {phase relaxation; diffuse interface; subdifferential operator; finite elements; semi-explicit Euler method; adaptivity; variable step-size; stability; a posteriori error estimates; numerical experiments; performance},
language = {eng},
number = {4},
pages = {775-797},
publisher = {Dunod},
title = {Error control and adaptivity for a phase relaxation model},
url = {http://eudml.org/doc/194012},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Chen, Zhiming
AU - Nochetto, Ricardo H.
AU - Schmidt, Alfred
TI - Error control and adaptivity for a phase relaxation model
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 4
SP - 775
EP - 797
LA - eng
KW - phase relaxation; diffuse interface; subdifferential operator; finite elements; semi-explicit Euler method; adaptivity; variable step-size; stability; a posteriori error estimates; numerical experiments; performance
UR - http://eudml.org/doc/194012
ER -

References

top
  1. [1] Z. Chen and R.H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527-548. Zbl0943.65075MR1742264
  2. [2] Z. Chen, R.H. Nochetto and A. Schmidt, Adaptive finite element methods for diffuse interface models (in preparation). 
  3. [3] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
  4. [4] Ph. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. Zbl0368.65008MR400739
  5. [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. Zbl0732.65093MR1083324
  6. [6] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. IV. Nonlinear problems. SIAM J. Numer. Anal. 32 (1995) 1729-1749. Zbl0835.65116MR1360457
  7. [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. Zbl0909.65063MR1620144
  8. [8] P. Grisvard, Elliptic Problems on Non-smooth Domains. Pitman, Boston (1985). Zbl0695.35060
  9. [9] X. Jiang and R.H. Nochetto, Optimal error estimates for semidiscrete phase relaxation models. RAIRO Model. Math. Anal. Numér. 31 (1997) 91-120. Zbl0874.65069MR1432853
  10. [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. Zbl0972.65067MR1619875
  11. [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. Zbl0934.65105MR1688994
  12. [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. Zbl0812.35166MR1285038
  13. [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. Zbl0944.65077MR1649189
  14. [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. Zbl1021.65047MR1737503
  15. [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. Zbl0942.65111MR1648399
  16. [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. Zbl0629.65130MR916294
  17. [17] C. Verdi and A. Visintin, Error estimates for a semi-explicit numerical scheme for Stefan-type problems. Numer. Math. 52 (1988) 165-185. Zbl0617.65125MR923709
  18. [18] A. Visintin, Stefan problem with phase relaxation. IMA J. Appl. Math. 34 (1985) 225-245. Zbl0585.35053MR804824
  19. [19] A. Visintin, Supercooling and superheating effects in phase transitions. IMA J. Appl. Math. 35 (1986) 233-256. Zbl0615.35090MR839201

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.