Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence rates of the DPG method with reduced test space degree   This paper presents a duality theorem of the Aubin-Nitsche type for
discontinuous Petrov Galerkin (DPG) methods. This explains the numerically
observed higher convergence rates in weaker norms. Considering the specific
example of the mild-weak (or primal) DPG method for the Laplace equation, two
further results are obtained. First, the DPG method continues to be solvable
even when the test space degree is reduced, provided it is odd. Second, a
non-conforming method of analysis is developed to explain the numerically
observed convergence rates for a test space of reduced degree.

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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th