This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.
J. E. Aarnes , On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation, SIAM J. Multiscale Modeling and Simulation, 2 (2004), pp. 421–439.
T. Arbogast , Analysis of a two-scale, locally conservative subgrid upscaling for elliptic problems, SIAM J. Numer. Anal., 42 (2004), pp. 576–598.
C.-C. Chu , I. Graham and T.-Y. Hou , A new multiscale finite element method for high-contrast elliptic interface problems, Math. Comp., 79 (2010), pp. 1915–1955.
E. Chung and W. T. Leung , A sub-grid structure enhanced discontinuous Galerkin method for multiscale diffusion and convection-diffusion problems, Comm. Comput. Phys., 14 (2013), pp. 370–392.
E. Chung , Y. Efendiev , and T. Y. Hou , Adaptive multiscale model reduction with generalized multiscale finite element methods, J. Comp. Phys., 320 (2016), pp. 69–95.
E. T. Chung and Y. Efendiev , Reduced-contrast approximations for high-contrast multiscale flow problems, Multiscale Modeling & Simulation, 8 (2010), pp. 1128–1153.
E. T. Chung , Y. Efendiev , and R. Gibson Jr., An energy-conserving discontinuous multiscale finite element method for the wave equation in heterogeneous media, Advances in Adaptive Data Analysis, 3 (2011), pp. 251–268.
E. T. Chung , Y. Efendiev , and C. S. Lee , Mixed generalized multiscale finite element methods and applications, Multiscale Model. Simul., 13 (2015), pp. 338–366.
E. T. Chung , Y. Efendiev , and W. T. Leung , Generalized multiscale finite element methods for wave propagation in heterogeneous media, Multiscale Modeling & Simulation, 12 (2014), pp. 1691–1721.
E. T. Chung , Y. Efendiev , and W. T. Leung , Residual-driven online generalized multiscale finite element methods, J. Comp. Phys., 302 (2015), pp. 176–190.
E. T. Chung , Y. Efendiev , and G. Li , An adaptive GMsFEM for high-contrast flow problems, J. Comp. Phys., 273 (2014), pp. 54–76.
E.T. Chung , Y. Efendiev , and S. Fu , Generalized multiscale finite element method for elasticity equations, International Journal on Geomathematics, 5 (2014), pp. 225–254.
L. J. Durlofsky , Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water resources research, 27 (1991), pp. 699–708.
Y. Efendiev , J. Galvis , and X.-H. Wu , Multiscale finite element methods for high-contrast problems using local spectral basis functions, J. Comp. Phys., 230 (2011), pp. 937–955.
K. Gao , E. T. Chung , R. Gibson , S. Fu and Y. Efendiev , A numerical homogeneization method for heterogenous, anisotropic elastic media based on multiscale theory, Geophysics, 80 (2015), pp. D385–D401.
K. Gao , S. Fu , R. Gibson , E. T. Chung and Y. Efendiev , Generalized multiscale finite element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, J. Comput. Phys., 295 (2015), pp. 161–188.
M. Ghommem , M. Presho , V. M. Calo and Y. Efendiev , Mode decomposition methods for flows in high-contrast porous media. Global–local approach, J. Comp. Phys., 253 (2013), pp. 226–238.
R. Gibson , K. Gao , E. Chung and Y. Efendiev , Multiscale modeling of acoustic wave propagation in two-dimensional media, Geophysics, 79 (2014), pp. T61–T75.
T. Y. Hou and X.-H. Wu , A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comp. Phys., 134 (1997), pp. 169–189.
P. Jenny , S.-H. Lee and H. Tchelepi , Multi-scale finite volume method for elliptic problems in subsurface flow simulation, J. Comput. Phys., 187 (2003), pp. 47–67.
X.-H. Wu , Y. Efendiev and T.-Y. Hou , Analysis of upscaling absolute permeability, Discrete and Continuous Dynamical Systems Series B, 2 (2002), pp. 185–204.