Full discretization of wave equation

Chaoui, A.; Ellaggoune, Fateh; Guezane-Lakoud, A.

doi:10.1186/s13661-015-0396-3

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…This theory has been extensively applied to elliptic and parabolic problems in the context of finite element approximation, as evidenced by various studies [27,6,12,4,3,7,13,14,18,19,20,28,17]. However, the a posteriori analysis of hyperbolic problems, whether using the finite element method or the spectral element method, remains relatively unexplored in the literature [5,10,11,16,24,25,15,1,2].…”

Section: Introductionmentioning

confidence: 99%

The posteriori analysis of the spectral element discretization of the wave equation

chorfi

2024

Preprint

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This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral elements method for spatial discretization. We prove that optimal adaptivity can be achieved by combining adaptive time steps with adaptive spectral mesh. We introduce two sets of error indicators for time and space, respectively, and derive optimal estimates.

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Section: Introductionmentioning

confidence: 99%

The posteriori analysis of the spectral element discretization of the wave equation

chorfi

2024

Preprint

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“…Elliptic, and parabolic problems have been widely developed by this theory in the context of the finite element approximation [27,6,12,4,3], and [7,13,14,18,19,20,28,17]. However, the a posteriori analysis of hyperbolic problems either by the finite element method or by the spectral element method has not been well addressed in the literature [5,10,11,16,24,25,15,1,2].…”

Section: Introductionmentioning

confidence: 99%

On the adaptivity analysis of the wave equation

Mustafa,

Nejmeddine,

Mohamed

2023

AUCMCS

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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.

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