The multi-scale-finite-volume (MSFV) procedure for the approximate solution of elliptic problems with varying coefficients has been recently modified by introducing an iterative loop to achieve any desired level of accuracy (iterative MSFV, IMSFV). We further develop the iterative concept considering a Galerkin approach to define the coarse-scale problem, which is one of the key elements of the MSFV and IMSFV-methods. The new Galerkin based method is still a multi-scale approach, in the sense that upscaling to the coarse-scale problem is achieved by means of numerically computed basis functions resulting from localized problems. However, it does not enforce strict conservativity at the coarse-scale level, and consequently no conservative velocity field can be defined as in the IMSFV-procedure until convergence to the exact solution is achieved. Numerical results are provided to evaluate the performance of the modified procedure.
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