Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residual-based variational multiscale modeling in a discontinuous
  Galerkin framework   We develop the general form of the variational multiscale method in a
discontinuous Galerkin framework. Our method is based on the decomposition of
the true solution into discontinuous coarse-scale and discontinuous fine-scale
parts. The obtained coarse-scale weak formulation includes two types of
fine-scale contributions. The first type corresponds to a fine-scale volumetric
term, which we formulate in terms of a residual-based model that also takes
into account fine-scale effects at element interfaces. The second type consists
of independent fine-scale terms at element interfaces, which we formulate in
terms of a new fine-scale "interface model". We demonstrate for the
one-dimensional Poisson problem that existing discontinuous Galerkin
formulations, such as the interior penalty method, can be rederived by choosing
particular fine-scale interface models. The multiscale formulation thus opens
the door for a new perspective on discontinuous Galerkin methods and their
numerical properties. This is demonstrated for the one-dimensional
advection-diffusion problem, where we show that upwind numerical fluxes can be
interpreted as an ad hoc remedy for missing volumetric fine-scale terms.

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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat