Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiscale methods for problems with complex geometry   We propose a multiscale method for elliptic problems on complex domains, e.g.
domains with cracks or complicated boundary. For local singularities this paper
also offers a discrete alternative to enrichment techniques such as XFEM. We
construct corrected coarse test and trail spaces which takes the fine scale
features of the computational domain into account. The corrections only need to
be computed in regions surrounding fine scale geometric features. We achieve
linear convergence rate in energy norm for the multiscale solution. Moreover,
the conditioning of the resulting matrices is not affected by the way the
domain boundary cuts the coarse elements in the background mesh. The analytical
findings are verified in a series of numerical experiments.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol