Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite
  Element Methods for the Von K\'arm\'an Equations   This paper analyses discontinuous Galerkin finite element methods (DGFEM) to
approximate a regular solution to the von K\'arm\'an equations defined on a
polygonal domain. A discrete inf-sup condition sufficient for the stability of
the discontinuous Galerkin discretization of a well-posed linear problem is
established and this allows the proof of local existence and uniqueness of a
discrete solution to the non-linear problem with a Banach fixed point theorem.
The Newton scheme is locally second-order convergent and appears to be a robust
solution strategy up to machine precision. A comprehensive a priori and a
posteriori energy-norm error analysis relies on one sufficiently large
stabilization parameter and sufficiently fine triangulations. In case the other
stabilization parameter degenerates towards infinity, the DGFEM reduces to a
novel $C^0$ interior penalty method (IPDG). Moreover, a reliable and efficient
a posteriori error analysis immediately follows for the DGFEM of this paper,
while the different norms in the known $C^0$-IPDG lead to complications with
some non-residual type remaining terms. Numerical experiments confirm the
best-approximation results and the equivalence of the error and the error
estimators. A related adaptive mesh-refining algorithm leads to optimal
empirical convergence rates for a non convex domain.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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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: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con