Abdulle, AssyrPouchon, Timothée Noé2015-06-152015-06-152015-06-15201610.1137/15M1025633https://infoscience.epfl.ch/handle/20.500.14299/115110WOS:000385026000009A fully discrete a priori analysis of the finite element heterogeneous multiscale method introduced in [A. Abdulle, M. Grote, and C. Stohrer, Multiscale Model. Simul., 12, 2014, pp. 1135-1166] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over long time is a Boussinesq-type equation that has been shown to approximate the one-dimensional multiscale wave equation with epsilon-periodic coefficients up to time O(epsilon(-2)) in [A. Lamacz, Math. Models Methods Appl. Sci., 21, 2011, pp. 1871-1899]. In this paper we also revisit this result by deriving and analyzing a family of effective Boussinesq-type equations for the approximation of the multiscale wave equation that depends on the normalization chosen for certain micro functions used to define the macroscopic models.a priori error analysismultiscale methodheterogeneous mediaeffective equationswave equationlong time behaviordispersive wavestext::journal::journal article::research article