A posteriori analysis of the spectral element discretization of heat equation

[1] M. Ainsworth, J.T. Oden, A procedure for a posteriori error estimation for h-p finite element methods, Comp. Methods in Applied Mech. and Eng. 101 (1992); 73-96.10.1016/0045-7825(92)90016-DSearch in Google Scholar

[2] I. Babuška, W.C. Rheinboldt, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Eng. 12 (1978); 1597-1645.10.1002/nme.1620121010Search in Google Scholar

[3] A. Bergam, C. Bernardi, Z. Mghazli, A posteriori analysis of the finite element discretization of some parabolic equations, Math. Comput., Vol 74, 1117-1138, (2005).10.1090/S0025-5718-04-01697-7Search in Google Scholar

[4] C. Bernardi, Indicateurs d’erreur en h−N version des éléments spectraux, to appear in Modèl. Math. et Anal. Numr. (1995).10.1051/m2an/1996300100011Search in Google Scholar

[5] C. Bernardi, Y. Maday, Approximation spectrales de problèmes aux limites elliptiques, Springer-Verlag, Berlin (1992).Search in Google Scholar

[6] C. Bernardi, B. Métivet, R. Verfürth - Analyse numrique d’indicateurs d’erreur, in Maillage et adaptation, P.-L. George ed., Hermès (2001); 251-278.Search in Google Scholar

[7] C. Bernardi, N. Chorfi, Spectral discretization of the vorticity velocity and pressure formulation of the Stokes problem, SIAM J. Numer. Anal., vol 44 pp. 826-850, (2006).10.1137/050622687Search in Google Scholar

[8] C. Johnson, Y.-Y. Nie, V. Thomée - An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem, SIAM J. Numer. Anal. 27, (1990); 277-291.10.1137/0727019Search in Google Scholar

[9] J.T. Oden, L. Demkowicz, W. Rachowicz, T.A. Westermann, Toward a universal h-p adaptive finite element strategy, Part II: a posteriori error estimation, Comp. Methods Appl. Mech. and Eng. 77 (1989); 113-180.10.1016/0045-7825(89)90130-8Search in Google Scholar

[10] J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod (1968).Search in Google Scholar

[11] V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics 25, Springer (1997).10.1007/978-3-662-03359-3Search in Google Scholar

[12] R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley et Teubner (1996).Search in Google Scholar

[13] R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques, J. Comput. Appl. Math. 50 (1994); 67-83.10.1016/0377-0427(94)90290-9Search in Google Scholar

[14] R. Verfürth, A posteriori error estimators and adaptive mesh-refinement techniques for the Navier-Stokes equations, in Incomputational Fluid Dynamics, Trends and Advances, M.D. Gunzburger and R.A. Nicolaides, Cambridge University Press (1993), 447-477.10.1017/CBO9780511574856.015Search in Google Scholar

[15] R. Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations, Math.Comput. 62 (1994); 445-475.10.1090/S0025-5718-1994-1213837-1Search in Google Scholar