Adaptive finite elements for a linear parabolic problem

Computer Methods in Applied Mechanics and Engineering

Volumn 167, Issue 3-4, 1998, Pages 223-237

  Picasso, Marco ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; ERROR ANALYSIS; PROBLEM SOLVING;

A POSTERIORI ERROR ESTIMATES; ADAPTIVE FINITE ELEMENTS; DELAUNAY TRIANGULATIONS; LINEAR PARABOLIC PROBLEM;

FINITE ELEMENT METHOD;

EID: 0032308963     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00121-2     Document Type: Article

References (23)

1. [1] M. Ainsworth and J.T. Oden, A unified approach to a posteriori error estimation using finite element residual methods, Numer. Math. 65 (1993) 23-50.
2. [2] E. Anderson, Z. Bai, C. Bischof, J. Demmal, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrou Chov and D. Soresen, LAPACK User;s Guide. SIAM, 3600 University City Science Center, Philadelphia, PA 19104-2688, 1992.
3. [3] I. Babuska, R. Duran and R. Rodriguez, Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements, SIAM J. Numer. Anal. 29(4) (1992) 947-964.
4. [4] I. Babuska and W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736-754.
5. [5] I. Babuska and W.C. Rheinboldt, A posteriori error estimators in the finite element method, Int. J. Numer. Methods Engrg. 12 (1978) 1597-1615.
6. [6] I. Babuska, T. Strouboulis and C.S. Upadhyay, A model study of the quality of a posteriori estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles, Comput. Methods Appl. Mech. Engrg. 114(4) (1994) 307-378.
7. [7] J. Baranger and H, El-Amri, Estimateurs a posteriori d'erreur pour le calcul adaptatif d'écoulements quasi-newtoniens, RAIRO M2AN 25(1) (1991) 31-48.
8. [8] C. Bernardi, Optimal finite element interpolation on curved domains, SIAM J. Numer. Anal. 26(5) (1989) 1212-1240.
9. [9] G. Caloz and J. Rappaz, Numerical analysis for nonlinear and bifurcation problems, in: P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis, Vol. 5 (Part 2) (North-Holland, Amsterdam, 1997) 487-638.
10. [10] P.G. Ciarlet, The Finite Element Method for Elliptic Problems (Academic Press, London, 1990).
11. [11] P. Clément, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9 (1975) 77-84.
12. [12] R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, INSTN-CEA collection enseignement. Masson, Paris, 1988.
13. [13] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. Numer. Anal. 28(1) (1991) 43-77.
14. [14] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems IV: nonlinear problems. Technical Report 44, Department of Mathematics, Chalmers University of Technology, the University of Göteborg, S-412 96 Göteborg, Sweden, 1992.
15. [15] K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems, Math. Comput. 60(201) (1993) 167-188.
16. [16] C. Johnson, Adaptive finite element methods for diffusion and convection problem, Comput. methods Appl. Mech. Engrg. 82 (1990) 301-322.
17. [17] J. Medina, M. Picasso and J. Rappaz, Error estimates and adaptive finite elements for nonlinear diffusion-convection problems, Math. Models Methods Appl. Sci. 6(5) (1966) 689-712.
18. [18] M. Picasso, An adaptive finite element algorithm for a two-dimensional stationary stefan-like problem, Comput. Methods Appl. mech. Engrg. 124 (1995) 213-230.
19. [19] J. Pousin and J. Rappaz, Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems, Numer. Math. 69(2) (1994) 213-232.
20. [20] S.W. Sloan, A fast algorithm for constructing Delaunay triangulations in the plane, Adv. Engrg. Software 9(1) (1987) 34-55.
21. [21] R. Verfürth, A posteriori error estimators for the Stokes equations, Numer. Math. 55 (1989) 309-325.
22. [22] R. Verfürth, A posteriori error estimates for nonlinear problems, finite element discretizations of elliptic equations, Math. Comput. 62(206) (1994) 445-475.
23. [23] R. Verfürth, A posteriori error estimates for nonlinear problems, finite element discretizations of parabolic equations, Technical Report 180, Fakultät Für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, 1995.