Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cookbook for finite element methods for nonlocal problems, including
  quadrature rules and approximate Euclidean balls   The implementation of finite element methods (FEMs) for nonlocal models with
a finite range of interaction poses challenges not faced in the partial
differential equations (PDEs) setting. For example, one has to deal with weak
forms involving double integrals which lead to discrete systems having higher
assembly and solving costs due to possibly much lower sparsity compared to that
of FEMs for PDEs. In addition, one may encounter non-smooth integrands. In many
nonlocal models, nonlocal interactions are limited to bounded neighborhoods
that are ubiquitously chosen to be Euclidean balls, resulting in the challenge
of dealing with intersections of such balls with the finite elements. We focus
on developing recipes for the efficient assembly of FEM stiffness matrices and
on the choice of quadrature rules for the double integrals that contribute to
the assembly efficiency and also posses sufficient accuracy. A major feature of
our recipes is the use of approximate balls, e.g., several polygonal
approximations of Euclidean balls, that, among other advantages, mitigate the
challenge of dealing with ball-element intersections. We provide numerical
illustrations of the relative accuracy and efficiency of the several approaches
we develop.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph