Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A narrow-stencil framework for convergent numerical approximations of
  fully nonlinear second order PDEs   This paper develops a unified general framework for designing convergent
finite difference and discontinuous Galerkin methods for approximating
viscosity and regular solutions of fully nonlinear second order PDEs. Unlike
the well-known monotone (finite difference) framework, the proposed new
framework allows for the use of narrow stencils and unstructured grids which
makes it possible to construct high order methods. The general framework is
based on the concepts of consistency and g-monotonicity which are both defined
in terms of various numerical derivative operators. Specific methods that
satisfy the framework are constructed using numerical moments. Admissibility,
stability, and convergence properties are proved, and numerical experiments are
provided along with some computer implementation details.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int