Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Kernel-Based Explicit Unconditionally Stable Scheme for
  Hamilton-Jacobi Equations on Nonuniform Meshes   In \cite{christlieb2019kernel}, the authors developed a class of high-order
numerical schemes for the Hamilton-Jacobi (H-J) equations, which are
unconditionally stable, yet take the form of an explicit scheme. This paper
extends such schemes, so that they are more effective at capturing sharp
gradients, especially on nonuniform meshes. In particular, we modify the
weighted essentially non-oscillatory (WENO) methodology in the previously
developed schemes by incorporating an exponential basis and adapting the
previously developed nonlinear filters used to control oscillations. The main
advantages of the proposed schemes are their effectiveness and simplicity,
since they can be easily implemented on higher-dimensional nonuniform meshes.
We perform numerical experiments on a collection of examples, including H-J
equations with linear, nonlinear, convex and non-convex Hamiltonians. To
demonstrate the flexibility of the proposed schemes, we also include test
problems defined on non-trivial geometry.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph