References
- [1] M. Abdelwahed, N. Chorfi, A posteriori analysis of the spectral element discretization of a non linear heat equation. Adv. Nonlinear Anal. 2021; 10: 477–490.10.1515/anona-2020-0140
- [2] M. Abdelwahed, N. Chorfi, On the convergence analysis of a time dependent elliptic equation with discontinuous coe cients. Adv. Nonlinear Anal. 2020; 9: 1145–1160.10.1515/anona-2020-0043
- [3] S. Adjerid, A posteriori finite element error estimation for second–order hyperbolic problems. Comput. Methods Appl. Mech. Engrg. 191 (2002), 4699–4719.
- [4] A. Bergam, C. Bernardi, Z. Mghazli, A posteriori analysis of the finite element discretization of some parabolic equations. Math. Comp. 74 (2005), no. 251, 1117–1138.
- [5] C. Bernardi, Y. Maday, Spectral Methods. in Handbook of Numerical Analysis V, P.G. Ciarlet and J.-L. Lions, eds., North–Holland, Amsterdam, 1997, pp. 209–485.10.1016/S1570-8659(97)80003-8
- [6] C. Bernardi, Y. Maday, F. Rapetti, Discrétisations variationnelles de problèmes aux limites elliptiques. Collection Mathématiques et Application, 45, Springer-Verlag, Paris, 2004.
- [7] W. Bangerth, R. Rannacher, Finite element approximation of the acoustic wave equation: error control and mesh adaptation. East-West J. Numer. Math. 7 (1999), 263–282.
- [8] W. Bangerth, R. Rannacher, Adaptive finite element techniques for the acoustic wave equation. J. Comput. Acoust. 9 (2001), 575–591.
- [9] C. Bernardi, E. Süli, Time and space adaptivity for the second-order wave equation. Math. Models Methods Appl. Sci. 15(2), 199–225 (2005)10.1142/S0218202505000339
- [10] A. Chaoui1, F. Ellaggoune2, A. Guezane-Lakoud, Full discretization of wave equation. Boundary Value Problems (2015) 2015:133 DOI 10.1186/s13661-015-0396-3
- [11] Y. Daikh, W. Chikouche, Spectral element discretization of the heat equation with variable di usion coe cient. HAL Id: hal-01143558, https://hal.archives-ouvertes.fr/hal-01143558, Apr 2015.
- [12] J.L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, 1968.
- [13] A. T. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys., 54, 468–488 (1984).
- [14] E. Süli, A posteriori error analysis and global error control for adaptive finite volume approximations of hyperbolic problems. Numerical Analysis 1995 (Dundee 1995), 169–190, Pitman Res. Notes Math. Ser. 344. Longman, Harlow (1996).
- [15] E. Süli, A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems. In: D. Kröner, M. Ohlberger and C. Rohde (Eds.) An Introduction to Recent Developments in Theory and Numerics for Conservation Laws. Lecture Notes in Computational Science and Engineering Volume 5, 123–194, Springer-Verlag (1998).