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Robert Altmann1, Eric Chung2, Roland Maier3, Daniel Peterseim3, Sai-Mang Pun4
[1] M.A. Biot, General theory of three-dimensional consolidation. J. Appl. Phys., 12:2(1941), 155-164.[2] D.L. Brown, J. Gedicke, and D. Peterseim, Numerical homogenization of heterogeneous fractional Laplacians. Multiscale Model. Simul., 16:3(2018), 1305-1332.[3] D.L. Brown and D. Peterseim, A multiscale method for porous microstructures. Multiscale Model. Simul., 14(2016), 1123-1152.[4] D.L. Brown and M. Vasilyeva, A generalized multiscale finite element method for poroelasticity problems I:Linear problems. J. Comput. Appl. Math., 294(2016), 372-388.[5] D.L. Brown and M. Vasilyeva, A generalized multiscale finite element method for poroelasticity problems II:Nonlinear coupling. J. Comput. Appl. Math., 297(2016), 132-146.[6] A. Caiazzo and J. Mura, Multiscale modeling of weakly compressible elastic materials in the harmonic regime and applications to microscale structure estimation. Multiscale Model. Simul., 12:2(2014), 514-537.[7] E.T. Chung, Y. Efendiev, and W.T. Leung, Constraint energy minimizing generalized multiscale finite element method. Comput. Method. Appl. M., 339(2018), 298-319.[8] E.T. Chung, Y. Efendiev, and W.T. Leung. Fast online generalized multiscale finite element method using constraint energy minimization. J. Comput. Phys., 355(2018), 450-463.[9] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.[10] P.G. Ciarlet, Mathematical elasticity. Vol. I. North-Holland, Amsterdam, 1988.[11] Y. Efendiev, J. Galvis, and T.Y. Hou, Generalized multiscale finite element methods (GMsFEM). J. Comput. Phys., 251(2013), 116-135.[12] C. Engwer, P. Henning, A. Målqvist, and D. Peterseim, Efficient implementation of the localized orthogonal decomposition method. ArXiv e-prints, 1602.01658, accepted for publication in Comp. Meth. Appl. Mech. Eng., 2019.[13] A. Ern and S. Meunier, A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems. ESAIM Math. Model. Numer. Anal., 43:2(2009), 353-375.[14] D. Gallistl and D. Peterseim, Computation of quasi-local effective diffusion tensors and connections to the mathematical theory of homogenization. Multiscale Model. Simul., 15:4(2017), 1530-1552.[15] F. Hellman, Gridlod. https://github.com/fredrikhellman/gridlod,2017. GitHub repository, commit 3e9cd20970581a32789aa1e21d7ff3f7e8f0b334.[16] P. Henning and D. Peterseim, Oversampling for the multiscale finite element method. Multiscale Model. Simul., 11:4(2013), 1149-1175.[17] R. Kornhuber, D. Peterseim, and H. Yserentant, An analysis of a class of variational multiscale methods based on subspace decomposition. Math. Comp., 87(2018), 2765-2774.[18] R. Kornhuber and H. Yserentant. Numerical homogenization of elliptic multiscale problems by subspace decomposition. Multiscale Model. Simul., 14:3(2016), 1017-1036.[19] A. Målqvist and A. Persson, A generalized finite element method for linear thermoelasticity. ESAIM Math. Model. Numer. Anal., 51:4(2017), 1145-1171.[20] A. Målqvist and A. Persson, Multiscale techniques for parabolic equations. Numer. Math., 138:1(2018), 191-217.[21] A. Målqvist and D. Peterseim, Localization of elliptic multiscale problems. Math. Comp., 83:290(2014), 2583-2603.[22] J. Mura and A. Caiazzo, A Two-Scale Homogenization Approach for the Estimation of Porosity in Elastic Media. Springer International Publishing, Cham, 2016, 89-105.[23] D. Peterseim, Variational multiscale stabilization and the exponential decay of fine-scale correctors. In Building Bridges:Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Springer, 2016, 341-367.[24] D. Peterseim and R. Scheichl, Robust numerical upscaling of elliptic multiscale problems at high contrast. Comput. Methods Appl. Math., 16:4(2016), 579-603.[25] R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl., 251:1(2000), 310-340.[26] M.D. Zoback, Reservoir Geomechanics. Cambridge University Press, Cambridge, 2010. |
[1] | Zhongyi Huang, Xu Yang. TAILORED FINITE CELL METHOD FOR SOLVING HELMHOLTZ EQUATION IN LAYERED HETEROGENEOUS MEDIUM [J]. Journal of Computational Mathematics, 2012, 30(4): 381-391. |
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