Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Scale Method for the Monge-Amp\`ere Equation: Convergence to the
  Viscosity Solution   We propose a two-scale finite element method for the Monge-Amp\`ere equation
with Dirichlet boundary condition in dimension $d\ge2$ and prove that it
converges to the viscosity solution uniformly. The method is inspired by a
finite difference method of Froese and Oberman, but is defined on unstructured
grids and relies on two separate scales: the first one is the mesh size $h$ and
the second one is a larger scale that controls appropriate directions and
substitutes the need of a wide stencil. The main tools for the analysis are a
discrete comparison principle and discrete barrier functions that control the
behavior of the discrete solution, which is continuous piecewise linear, both
close to the boundary and in the interior of the domain.

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The categories of this paper are: hep-th
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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: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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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: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an