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

This paper concerns the space/ time convergence analysis of conservative two-step 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. 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. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license.