Space/Time convergence analysis of a class of conservative schemes for linear wave equations

Juliette Chabassier 1 Sebastien Imperiale 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : This paper concerns the space/time convergence analysis of conservative two-steps time discretizations for linear wave equations. Explicit and implicit, second and fourth order schemes are considered, while the space discretization is given and satisfies minimal hypotheses. The convergence analysis is done using energy techniques and holds if the time step is upper-bounded by a quantity depending on space discretization parameters. In addition to showing the convergence for recently introduced fourth order schemes, the novelty of this work consists in the independency of the convergence estimates with respect to the difference between the time step and its greatest admissible value.
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Juliette Chabassier, Sebastien Imperiale. Space/Time convergence analysis of a class of conservative schemes for linear wave equations. Comptes Rendus Mathématique, Elsevier Masson, 2017, 355 (3), pp.282-289. ⟨10.1016/j.crma.2016.12.009⟩. ⟨hal-01421882⟩

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