We examine the composition of the
norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the
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We examine the composition of the
norm with weakly
convergent sequences of gradient fields associated with the homogenization of second order
divergence form partial differential equations with measurable coefficients. Here the
sequences of coefficients are chosen to model heterogeneous media and are piecewise
constant and highly oscillatory. We identify local representation formulas that in the
fine phase limit provide upper bounds...
A multiscale spectral generalized finite element method (MS-GFEM) is presented for the solution of large two and three dimensional stress analysis problems inside heterogeneous media. It can be employed to solve problems too large to be solved directly with FE techniques and is designed for implementation on massively parallel machines. The method is multiscale in nature and uses an optimal family of spectrally defined local basis functions over a coarse grid. It is proved that the method has an...
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