Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Stable and High-Order Accurate Discontinuous Galerkin Based Splitting
  Method for the Incompressible Navier-Stokes Equations   In this paper we consider discontinuous Galerkin (DG) methods for the
incompressible Navier-Stokes equations in the framework of projection methods.
In particular we employ symmetric interior penalty DG methods within the
second-order rotational incremental pressure correction scheme. The major focus
of the paper is threefold: i) We propose a modified upwind scheme based on the
Vijayasundaram numerical flux that has favourable properties in the context of
DG. ii) We present a novel postprocessing technique in the Helmholtz projection
step based on $H(\text{div})$ reconstruction of the pressure correction that is
computed locally, is a projection in the discrete setting and ensures that the
projected velocity satisfies the discrete continuity equation exactly. As a
consequence it also provides local mass conservation of the projected velocity.
iii) Numerical results demonstrate the properties of the scheme for different
polynomial degrees applied to two-dimensional problems with known solution as
well as large-scale three-dimensional problems. In particular we address
second-order convergence in time of the splitting scheme as well as its
long-time stability.

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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat