Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An advection-robust Hybrid High-Order method for the Oseen problem   In this work, we study advection-robust Hybrid High-Order discretizations of
the Oseen equations. For a given integer $k\ge 0$, the discrete velocity
unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements
and faces, while the pressure unknowns are discontinuous polynomials of total
degree $\le k$ on the mesh. From the discrete unknowns, three relevant
quantities are reconstructed inside each element: a velocity of total degree
$\le(k+1)$, a discrete advective derivative, and a discrete divergence. These
reconstructions are used to formulate the discretizations of the viscous,
advective, and velocity-pressure coupling terms, respectively. Well-posedness
is ensured through appropriate high-order stabilization terms. We prove energy
error estimates that are advection-robust for the velocity, and show that each
mesh element $T$ of diameter $h_T$ contributes to the discretization error with
an $\mathcal{O}(h_T^{k+1})$-term in the diffusion-dominated regime, an
$\mathcal{O}(h_T^{k+\frac12})$-term in the advection-dominated regime, and
scales with intermediate powers of $h_T$ in between. Numerical results complete
the exposition.

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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph