Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discontinuous Skeletal Gradient Discretisation Methods on polytopal
  meshes   In this work we develop arbitrary-order Discontinuous Skeletal Gradient
Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal
refers to the fact that the globally coupled unknowns are broken polynomial on
the mesh skeleton. The key ingredient is a high-order gradient reconstruction
composed of two terms: (i) a consistent contribution obtained mimicking an
integration by parts formula inside each element and (ii) a stabilising term
for which sufficient design conditions are provided. An example of
stabilisation that satisfies the design conditions is proposed based on a local
lifting of high-order residuals on a Raviart-Thomas-N\'ed\'elec subspace. We
prove that the novel DSGDs satisfy coercivity, consistency, limit-conformity,
and compactness requirements that ensure convergence for a variety of elliptic
and parabolic problems. Links with Hybrid High-Order, non-conforming Mimetic
Finite Difference and non-conforming Virtual Element methods are also studied.
Numerical examples complete the exposition.

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The categories of this paper are: math-ph
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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: physics
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph