Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Posteriori Error Estimation of hp-dG Finite Element Methods for Highly
  Indefinite Helmholtz Problems (extended version)   In this paper, we will consider an $hp$-finite elements discretization of a
highly indefinite Helmholtz problem by some dG formulation which is based on
the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will
introduce an a posteriori error estimator and derive reliability and efficiency
estimates which are explicit with respect to the wavenumber and the
discretization parameters $h$ and $p$. In contrast to the conventional
conforming finite element method for indefinite problems, the dG formulation is
unconditionally stable and the adaptive discretization process may start from a
very coarse initial mesh. Numerical experiments will illustrate the efficiency
and robustness of the method.

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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin