A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension

Numerische Mathematik

Volumn 83, Issue 3, 1999, Pages 455-475

  Segeth, K ^a  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033413802     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050459     Document Type: Article

References (16)

1. Adjerid, S., Flaherty, J. E. (1986): A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations. SIAM J. Numer. Anal. 23, 778-796
2. Adjerid, S., Flaherty, J. E. (1988): A local refinement finite element method for two-dimensional parabolic systems. SIAM J. Sci. Statist. Comput. 9, 792-810
3. Adjerid, S., Flaherty, J. E., Wang, Y. J. (1993): A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. Numer. Math. 65, 1-21
4. Babuška, I., Strouboulis, T., Upadhyay, C. S., Gangaraj, S. K. (1995): A posteriori error estimation and adaptive control of the pollution error in the h-version of the finite element method. Internat. J. Numer. Methods Engrg. 38, 4207-4235
5. Bieterman, M., Babuška, I. (1982): The finite element method for parabolic equations I, II. Numer. Math. 40, 339-371, 373-406
6. Coddington, E. A., Levinson, N. (1955): Theory of Ordinary Differential Equations. McGraw-Hill, New York
7. Eriksson, K., Johnson, C. (1991): Adaptive finite element methods for parabolic problems I. SIAM J. Numer. Anal. 28, 43-77
8. Eriksson, K., Johnson, C. (1995): Adaptive finite element methods for parabolic problems IV: Nonlinear problems. SIAM J. Numer. Anal. 32, 1729-1749
9. Moore, P. K. (1994): A posteriori error estimation with finite element semi- and fully discrete methods for nonlinear parabolic equations in one space dimension. SIAM J. Numer. Anal. 31, 149-169.
10. Moore, P. K., Flaherty, J. E. (1990): A local refinement finite element method for one-dimensional parabolic systems. SIAM J. Numer. Anal. 27, 1422-1444
11. Segeth, K. (1993): Grid adjustment based on a posteriori error estimators. Appl. Math. 38, 488-504
12. Segeth, K. (1994): A posteriori error estimates for parabolic differential systems solved by the finite element method of lines. Appl. Math. 39, 415-443
13. Segeth, K. (1995): Grid adjustment for parabolic systems based on a posteriori error estimates. J. Comput. Appl. Math. 63, 349-355
14. Segeth, K. (1995): Space grid adjustment for parabolic systems. In: Proceedings 1st International Conference on Difference Equations (San Antonio, TX, 1994), pp. 469-481. Gordon and Breach Publishers, Luxembourg
15. Szabó, B., Babuška, I. (1991): Finite Element Analysis. J. Wiley & Sons, New York
16. Thomée, V. (1997): Galerkin Finite Element Methods for Parabolic Problems. Springer, Berlin