Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A posteriori error estimates via equilibrated stress reconstructions for
  contact problems approximated by Nitsche's method   We present an a posteriori error estimate based on equilibrated stress
reconstructions for the finite element approximation of a unilateral contact
problem with weak enforcement of the contact conditions. We start by proving a
guaranteed upper bound for the dual norm of the residual. This norm is shown to
control the natural energy norm up to a boundary term, which can be removed
under a saturation assumption. The basic estimate is then refined to
distinguish the different components of the error, and is used as a starting
point to design an algorithm including adaptive stopping criteria for the
nonlinear solver and automatic tuning of a regularization parameter. We then
discuss an actual way of computing the stress reconstruction based on the
Arnold-Falk-Winther finite elements. Finally, after briefly discussing the
efficiency of our estimators, we showcase their performance on a panel of
numerical tests.

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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: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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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: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin