Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergent filtered schemes for the Monge-Amp\`ere partial differential
  equation   The theory of viscosity solutions has been effective for representing and
approximating weak solutions to fully nonlinear Partial Differential Equations
(PDEs) such as the elliptic Monge-Amp\`ere equation. The approximation theory
of Barles-Souganidis [Barles and Souganidis, Asymptotic Anal., 4 (1999)
271-283] requires that numerical schemes be monotone (or elliptic in the sense
of [Oberman, SIAM J. Numer. Anal, 44 (2006) 879-895]. But such schemes have
limited accuracy. In this article, we establish a convergence result for nearly
monotone schemes. This allows us to construct finite difference discretizations
of arbitrarily high-order. We demonstrate that the higher accuracy is achieved
when solutions are sufficiently smooth. In addition, the filtered scheme
provides a natural detection principle for singularities. We employ this
framework to construct a formally second-order scheme for the Monge-Amp\`ere
equation and present computational results on smooth and singular solutions.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga