Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pressure-induced locking in mixed methods for time-dependent
  (Navier-)Stokes equations   We consider inf-sup stable mixed methods for the time-dependent
incompressible Stokes and Navier--Stokes equations, extending earlier work on
the steady (Navier-)Stokes Problem. A locking phenomenon is identified for
classical inf-sup stable methods like the Taylor-Hood or the Crouzeix-Raviart
elements by a novel, elegant and simple numerical analysis and corresponding
numerical experiments, whenever the momentum balance is dominated by forces of
a gradient type. More precisely, a reduction of the $L^2$ convergence order for
high order methods, and even a complete stall of the $L^2$ convergence order
for lowest-order methods on preasymptotic meshes is predicted by the analysis
and practically observed. On the other hand, it is also shown that
(structure-preserving) pressure-robust mixed methods do not suffer from this
locking phenomenon, even if they are of lowest-order. A connection to
well-balanced schemes for (vectorial) hyperbolic conservation laws like the
shallow water or the compressible Euler equations is made.

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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con