Metric based upscaling

  title={Metric based upscaling},
  author={Houman Owhadi and Lei Zhang},
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
56 Citations
69 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 56 extracted citations


Publications referenced by this paper.
Showing 1-10 of 69 references

Elliptic and Parabolic Equations with Discontinuous Coefficients, volume

  • A. Maugeri, D. K. Palagachev, L. G. Softova
  • Mathematical Research. Wiley-VCH,
  • 2000
Highly Influential
5 Excerpts

Some results and examples about the behavior of harmonic functions and Green’s functions with respect to second order elliptic operators

  • Alano Ancona
  • Nagoya Math. J.,
  • 2002
Highly Influential
4 Excerpts

Compacité par compensation

  • François Murat
  • Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),
  • 1978
Highly Influential
3 Excerpts

Approximate inverse preconditioning of fe systems for elliptic operators with non-smooth coefficients

  • Mario Bebendorf
  • Preprint 7/2004,
  • 2005
2 Excerpts

Similar Papers

Loading similar papers…