Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the best constant matrix approximating an oscillatory matrix-valued
  coefficient in divergence-form operators   We approximate an elliptic problem with oscillatory coefficients using a
problem of the same type, but with constant coefficients. We deliberately take
an engineering perspective, where the information on the oscillatory
coefficients in the equation can be incomplete. A theoretical foundation of the
approach in the limit of infinitely small oscillations of the coefficients is
provided, using the classical theory of homogenization. We present a
comprehensive study of the implementation aspects of our method, and a set of
numerical tests and comparisons that show the potential practical interest of
the approach. The approach detailed in this article improves on an earlier
version briefly presented in [C. Le Bris, F. Legoll and K. Li, C. R. Acad. Sci.
Paris 2013].

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc