Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistency and Convergence of Finite Volume Approximations to Nonlinear
  Hyperbolic Balance Laws   This paper addresses the three concepts of \textit{ consistency, stability
and convergence } in the context of compact finite volume schemes for systems
of nonlinear hyperbolic conservation laws. The treatment utilizes the framework
of "balance laws". Such laws express the relevant physical conservation laws in
the presence of discontinuities. Finite volume approximations employ this
viewpoint, and the present paper can be regarded as being in this category. It
is first shown that under very mild conditions a weak solution is indeed a
solution to the balance law. The schemes considered here allow the computation
of several quantities per mesh cell (e.g., slopes) and the notion of
consistency must be extended to this framework. Then a suitable convergence
theorem is established, generalizing the classical convergence theorem of Lax
and Wendroff. Finally, the limit functions are shown to be entropy solutions by
using a notion of "Godunov compatibility", which serves as a substitute to the
entropy condition.

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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg