lndicateurs d'erreur pour I' equation de Ia chaleur
Keywords:
Heat equation, error indicators, a posteriori estimatesAbstract
In this paper, we recall the standard discretization of the two- or three-dimensional heat equation by finite elements and Euler's implicit scheme, together with its stability properties. Next we propose a familly of spatial error indicators which are built from the residual of the equation already discretized with respect to the time variable, and we prove that they satisfy some optimal estimates.
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References
[BBLM] C. BERNARDI, 0. BONNIN, C. LANGOUET, B. METIVET, "Residual error indicators
for linear problems. Extension to the Navier-Stokes equations", Proc.lnt. Conf. Finite
Elements in Fluids, Venezia, 1995,347-356.
[BG 1 C. BERNARDI, V. GIRAULT, "A local regularization operator for triangular and quadrilateral
finite elements", SIAM J. Numer. Anal., vol. 35, 1998, 1893-1916.
[BMV] C. BERNARDI, B. METIVET, R. VERFURTH, "Analyse numerique d'indicateurs d'erreur",
Rapport Interne 93025, Laboratoire d'Analyse Numerique de l'Universite Pierre et
Marie Curie, Paris, 1993.
[CL] P. CLEMENT, "Approximation by finite element functions using local regularization",
RAIRO Anal. Numer., vol. 9,1975,77--84.
]CR] M. CROUZEIX, P.-A. RAVIART, "Approximation des problemes d'evolution", Rapport
Interne de I 'Universite de Rennes, 1982.
]CT] M. CROUZEIX, V. THOMEE, "The stability in Lp and Wi of the £2-projection onto
finite element function spaces", Math. Comput., vol. 48, 1987,521-532.
]VEl] R. VERFiJRTH, "A posteriori error estimation and adaptive mesh-refinement techniques",
Comput. Appl. Math., vol. 50, 1994,67-83.
]VE2] R. VERFiJRTH, A Review of A Posteriori Error Estimation and Adaptive MeshRefinement
Techniques, Wiley & Teubner, 1996.
