A PRIORI ERROR ANALYSIS OF THE FINITE ELEMENT HETEROGENEOUS MULTISCALE METHOD FOR THE WAVE EQUATION OVER LONG TIME

作者：Abdulle Assyr^*; Pouchon Timothee

来源：SIAM Journal on Numerical Analysis, 2016, 54(3): 1507-1534.

DOI：10.1137/15M1025633

• a priori error analysis
• multiscale method
• heterogeneous media
• effective equations
• wave equation
• long time behavior
• dispersive waves

A 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.

• 出版日期2016