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A finite element heterogeneous multiscale method (FE-HMM) is proposed for the wave equation with highly oscillatory coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coefficients are computed on sampling domains at the micro scale within each macro finite element. Hence the computational work involved is independent of the highly heterogeneous nature of the medium at the smallest scale. Optimal errordoi:10.1137/100800488 fatcat:z6xlm7x3njfafdp7dpwv4jk7vy