Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonality relations of Crouzeix-Raviart and Raviart-Thomas finite
  element spaces   Identities that relate projections of Raviart-Thomas finite element vector
fields to discrete gradients of Crouzeix-Raviart finite element functions are
derived under general conditions. Various implications such as discrete convex
duality results and a characterization of the image of the projection of the
Crouzeix-Ravaiart space onto elementwise constant functions are deduced.

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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: stat