Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discontinuous Petrov-Galerkin boundary elements   Generalizing the framework of an ultra-weak formulation for a hypersingular
integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697
(to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular
integral equation on open and closed polyhedral surfaces. We develop a general
ultra-weak setting in fractional-order Sobolev spaces and prove its
well-posedness and equivalence with the traditional formulation. Based on the
ultra-weak formulation, we establish a discontinuous Petrov-Galerkin method
with optimal test functions and prove its quasi-optimal convergence in related
Sobolev norms. For closed surfaces, this general result implies quasi-optimal
convergence in the L^2-norm. Some numerical experiments confirm expected
convergence rates.

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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org