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Generalized FEM for Homogenization Problems
(2001)SAM Research ReportWe introduce the concept of generalized Finite Element Method (gFEM) for the numerical treatment of homogenization problems. These problems are characterized by highly oscillatory periodic (or patchwise periodic) pattern in the coefficients of the differential equation and their solutions exhibit a multiple scale behavior: a macroscopic behavior superposed with local characteristics at micro length scales. The gFEM is based on two-scale ...Report -
Two-Scale FEM for Homogenization Problems
(2001)SAM Research ReportThe convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale \e << 1 is analyzed. Full elliptic regularity independent of \e is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the \e scale of the solution with work independent of \e and without analytical homogenization are introduced. ...Report