Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Model Reduction by $L^1$-norm Minimization and Approximation via
  Dictionaries: Application to Linear and Nonlinear Hyperbolic Problems   We propose a novel model reduction approach for the approximation of non
linear hyperbolic equations in the scalar and the system cases. The approach
relies on an offline computation of a dictionary of solutions together with an
online $L^1$-norm minimization of the residual. It is shown why this is a
natural framework for hyperbolic problems and tested on nonlinear problems such
as Burgers' equation and the one-dimensional Euler equations involving shocks
and discontinuities. Efficient algorithms are presented for the computation of
the $L^1$-norm minimizer, both in the cases of linear and nonlinear residuals.
Results indicate that the method has the potential of being accurate when
involving only very few modes, generating physically acceptable,
oscillation-free, solutions.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys