Abstract
The purpose of this work deals with the discretization of a second order linear wave equation by the implicit Euler scheme in time and by the spectral elements method in space. We prove that the adaptivity of the time steps can be combined with the adaptivity of the spectral mesh in an optimal way. Two families of error indicators, in time and in space, are proposed. Optimal estimates are obtained.
Reference34 articles.
1. "[1] M. Abdelwahed and N. Chorfi, The spectral discretization of the second-order wave equation, An. St. Univ. Ovidius Constant. Vol. 30, (2022), No. 3, Page: 5-20.
2. [2] M. Abdelwahed and N. Chorfi, resolution of the wave equation using the spectral method, Boundary Value Problem Volume:2022, Issue: 1, Article Number: 15, (2022).
3. [3] M. Abdelwahed and N. Chorfi, A posteriori analysis of the spectral element discretization of a non linear heat equation, Adv. Nonlinear Anal. 10 (2021), 477-490.
4. [4] M. Abdelwahed and N. Chorfi, On the convergence analysis of a time dependent elliptic equation with discontinuous coefficients, Adv. Nonlinear Anal. 9 (2020), 1145-1160.
5. [5] S. Adjerid, A posteriori nite element error estimation for second order hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 191, (2002), 4699-4719.