Metric based upscaling

@inproceedings{Owhadi2005MetricBU,
  title={Metric based upscaling},
  author={Houman Owhadi and Lei Zhang},
  year={2005}
}
We consider divergence form elliptic operators in dimension n ≥ 2 with L∞ coefficients. Although solutions of these operators are only Hölder continuous, we show that they are differentiable (C1,α) with respect to harmonic coordinates. It follows that numerical homogenization can be extended to situations where the medium has no ergodicity at small scales and is characterized by a continuum of scales by transferring a new metric in addition to traditional averaged (homogenized) quantities from… CONTINUE READING
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