Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On explicit form of the FEM stiffness matrix for the integral fractional
  Laplacian on non-uniform meshes   We derive exact form of the piecewise-linear finite element stiffness matrix
on general non-uniform meshes for the integral fractional Laplacian operator in
one dimension, where the derivation is accomplished in the Fourier transformed
space. With such an exact formulation at our disposal, we are able to
numerically study some intrinsic properties of the fractional stiffness matrix
on some commonly used non-uniform meshes (e.g., the graded mesh), in
particular, to examine their seamless transition to those of the usual
Laplacian.

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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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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: q-bio