Error indicators for the mortar finite element discretization of a parabolic problem

Numerical Algorithms

Volumn 34, Issue 2-4, 2003, Pages 187-201

  Bergam, A ^a   Bernardi, C ^b   Hecht, F ^b   Mghazli, Z ^a  

^a IBN TOFAIL UNIVERSITY   (Morocco)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Finite elements; Mortar method; Parabolic equation

Indexed keywords

EID: 4043110638     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000005362.95126.4c     Document Type: Article

References (21)

1. I. Babuška, R. Duran and R. Rodriguez, Analysis of the efficiency of an a posteriori error estimator for linear triangular elements, SIAM J. Numer. Anal. 29 (1992) 947-964.
2. R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985) 283-301.
3. F. Ben Belgacem, The Mortar finite element method with Lagrange multipliers, Numer. Math. 84 (1999) 173-197.
4. F. Ben Belgacem, C. Bernardi, N. Chorfi and Y. Maday, Inf-sup conditions for the mortar spectral element discretization of the Stokes problem, Numer. Math. 85 (2000) 257-281.
5. A. Bergam, C. Bernardi and Z. Mghazli, A posteriori analysis of the finite element discretization of a nonlinear parabolic equation, submitted.
6. C. Bernardi and F. Hecht, Error indicators for the mortar finite element discretization of the Laplace equation, Math. Comp. 71 (2002) 1371-1402.
7. C. Bernardi and Y. Maday, Mesh adaptivity in finite elements by the mortar method, Rev. Européenne Éléments Finis 9 (2000) 451-465.
8. C. Bernardi, Y. Maday and A.T. Patera, Domain decomposition by the mortar element method, in: Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, eds. H.G. Kaper and M. Garbey, NATO Advanced Science Institutes Series C, Vol. 384 (Kluwer Academic, Dordrecht, 1993) pp. 269-286.
9. C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: The mortar element method, in: Collège de France Seminar, Vol. XI, eds. H. Brezis and J.-L. Lions (Pitman, London, 1994) pp. 13-51.
10. C. Bernardi and B. Métivet, Indicateurs d'erreur pour l'équation de la chaleur, Rev. Européenne Éléments Finis 9 (2000) 425-438.
11. M. Bieterman and I. Babuska, The finite element method for parabolic equations I, A posteriori error estimation, Numer. Math. 40 (1982) 339-371.
12. 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.
13. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems IV, Nonlinear problems, SIAM J. Numer. Anal. 32 (1995) 1729-1749.
14. F. Hecht and O. Pironneau, Multiple meshes and the implementation of Freefem+, Internal Report, I.N.R.I.A., Rocquencourt (1999).
15. R. Nochetto, G. Savaré and C. Verdi, A posteriori error estimates for variable time-step discretization of nonlinear evolution equations, Comm. Pure Appl. Math. 53 (2000) 525-589.
16. R. Verfürth, A posteriori estimators for the Stokes equations, Numer. Math. 55 (1989) 309-325.
17. R. Verfürth, FEMFLOW-user guide, version 1, Internal Report, Universität Zürich (1989).
18. R. Verfürth, A posteriori error estimator for nonlinear problem. Finite element discretizations of elliptic equations, Math. Comp. 62 (1994) 445-475.
19. R. Verfürth, A posteriori error estimates and adaptive mesh-refinement techniques, J. Comput. Appl. Math. 50 (1994) 67-83.
20. R. Verfürth, A posteriori error estimators and adaptive mesh-refinement for a mixed finite element discretization of the Navier-Stokes equations, in: Numerical Treatment of the Navier-Stokes Equations, eds. W. Hackbusch and R. Rannacher, Notes on Numerical Fluid Mechanics, Vol. 30 (Vieweg, Braunschweig, 1989) pp. 145-152.
21. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques (Wiley and Teubner, 1996).