An error estimate for a finite-element scheme for a phase field model

IMA Journal of Numerical Analysis

Volumn 14, Issue 2, 1994, Pages 243-255

  Chen, Zhiming ^a   Hoffmann, K H ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844497553     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/14.2.243     Document Type: Article

References (10)

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2. Caginalp, G. 1989 Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. Phys. Rev. 39, 5887-5891.
3. Caginalp, G., Lin, J. T. 1987 A numerical analysis of an anisotropic phase field model. IMA J. Appl. Math. 39, 51-66.
4. Chen, Z. 1992 Das phasenfeldmodell fur das problem der phaseniibergange: analysis, numerik und steuerung. Dissertation, University of Augsburg, Germany.
5. Ciarlet, P. G. 1978 The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
6. Elliott, C. M., Zheng, S. 1990 Global existence and stability of solutions to the phase field equations. Free boundary Value Problems (K.-H. Hoffmann et al, eds). Birkhauser.
7. Hoffmann, K.-H., Jiang, L. 1992 Optimal control problem for a phase field model. Numer. Funct. Anal. Optimization 13, 11-27.
8. Ji, C. 1989 Instability and pattern formation in phase field model. Dissertation, Clarkson University, USA.
9. Lin, J. T. 1988 The numerical analysis of a phase field model in moving boundary problems. SIAM. J. Numer. Anal. 25, 1015-1031.
10. Nie, Y.-Y., Thomse, V. 1985 A lumped mass finite-element method with quadrature for a nonlinear parabolic problem. IMA J. Numer. Anal. 5, 376-391.