Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divergence-conforming methods for transient doubly-diffusive flows: A
  priori and a posteriori error analysis   The analysis of the double-diffusion model and
$\mathbf{H}(\mathrm{div})$-conforming method introduced in [B\"urger, M\'endez,
Ruiz-Baier, SINUM (2019), 57:1318--1343] is extended to the time-dependent
case. In addition, the efficiency and reliability analysis of residual-based
{\it a posteriori} error estimators for the steady, semi-discrete, and fully
discrete problems is established. The resulting methods are applied to simulate
the sedimentation of small particles in salinity-driven flows. The method
consists of Brezzi-Douglas-Marini approximations for velocity and compatible
piecewise discontinuous pressures, whereas Lagrangian elements are used for
concentration and salinity distribution. Numerical tests confirm the properties
of the proposed family of schemes and of the adaptive strategy guided by the
{\it a posteriori} error indicators.

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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
23
The categories of this paper are: solv-int