Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales

Abstract The aim of this work is the numerical homogenization a parabolic problem with several time and spatial scales using heterogeneous multiscale method. We replace actual cell an alternate one, Dirichlet boundary initial values instead periodic conditions. Further, we give detailed priori error analysis fully discretized, i.e., in space for both macroscopic problem, Numerical experiments illustrate theoretical convergence rates.