
arXiv: 1604.08312
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
Multiscale, Physics and Astronomy (miscellaneous), Flows in porous media; filtration; seepage, Porous media, numerical homogenization, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, heterogeneous media, 510, Computer Science Applications, porous media, Multiscale finite element method, multiscale, FOS: Mathematics, Mathematics - Numerical Analysis, multiscale finite element method, Numerical homogenization, Heterogeneous media, Finite element methods applied to problems in fluid mechanics
Multiscale, Physics and Astronomy (miscellaneous), Flows in porous media; filtration; seepage, Porous media, numerical homogenization, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, heterogeneous media, 510, Computer Science Applications, porous media, Multiscale finite element method, multiscale, FOS: Mathematics, Mathematics - Numerical Analysis, multiscale finite element method, Numerical homogenization, Heterogeneous media, Finite element methods applied to problems in fluid mechanics
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