Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and approximation of a (regularized) Oldroyd-B model   Two finite element approximations of the Oldroyd-B model for dilute polymeric
fluids are considered, in bounded 2- and 3-dimensional domains, under no flow
boundary conditions. The pressure and the symmetric conformation tensor are
aproximated by either (a) piecewise constants or (b) continuous piecewise
linears, the velocity by (a) continuous piecewise quadratics or a reduced
version with linear tangential component on each edge, and (b) by continuous
piecewise quadratics or the mini-element. Both schemes (a) and (b) satisfy a
free energy bound, which involves the logarithm of the conformation tensor,
without any constraint on the time step for the backward Euler type time
discretization. This extends the results of [Boyaval et al. M2AN 43 (2009)
523--561], where a piecewise constant approximation of the conformation tensor
was necessary to treat the advection term in the stress equation, and a
restriction on the time step, based on the initial data, was required to ensure
that the approximation to the conformation tensor remained positive definite.
Furthermore, for (b) in the presence of an additional dissipative term in the
stress equation and a cut-off on the conformation tensor on certain terms like
in [Barrett and S\"uli, M3AS 18 (2008) 935--971] for the FENE dumbbell model,
we show (subsequence) convergence towards global-in-time weak solutions (when
d=2, cut-offs can be replaced with a time step restriction dependent on the
spatial discretization parameter). Hence, we prove existence of global-in-time
weak solutions to these regularized models.

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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg