Table 3.

Trial function library for nonlocal 1D example (Section 5.2).

Mean-field term	Trial function library
$\nabla \cdot (U\nabla K\ast U)$	$\nabla \cdot (U\nabla {\mid x\mid }^m\ast U)$, $m\in \{1,2,3,4,5,6,7\}$ {1, 2, 3, 4, 5, 6, 7}
$\nabla \cdot (U\nabla V)$	${\partial }_x(U{x}^m)$, $m\in \{0,2,3,4,5,6,7,8\}$ {0, 2, 3, 4, 5, 6, 7, 8}
$\frac{1}{2}{\sum }_{i,j=1}^d\frac{{\partial }^2{(U\sigma {\sigma }^T)}_{ij}}{\partial x_i\partial x_j}$	${\partial }_{xx}(U{x}^m)$, $m\in \{0,1,2,3,4,5,6,7,8\}$ {0, 1, 2, 3, 4, 5, 6, 7, 8}