A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
A hierarchical fracture model for the iterative multiscale finite volume method
Journal of Computational Physics
Algebraic multiscale solver for flow in heterogeneous porous media
Journal of Computational Physics
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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.