Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric based up-scaling   We consider divergence form elliptic operators in dimension $n\geq 2$ with
$L^\infty$ coefficients. Although solutions of these operators are only
H\"{o}lder continuous, we show that they are differentiable ($C^{1,\alpha}$)
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
subgrid scales into computational scales and error bounds can be given. This
numerical homogenization method can also be used as a compression tool for
differential operators.

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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: stat