1(common-notation)= 2 3# Common notation 4 5For most of our examples, the spatial discretization 6uses high-order finite elements/spectral elements, namely, the high-order Lagrange 7polynomials defined over $P$ non-uniformly spaced nodes, the 8Gauss-Legendre-Lobatto (GLL) points, and quadrature points $\{q_i\}_{i=1}^Q$, with 9corresponding weights $\{w_i\}_{i=1}^Q$ (typically the ones given by Gauss 10or Gauss-Lobatto quadratures, that are built in the library). 11 12We discretize the domain, $\Omega \subset \mathbb{R}^d$ (with $d=1,2,3$, 13typically) by letting $\Omega = \bigcup_{e=1}^{N_e}\Omega_e$, with $N_e$ 14disjoint elements. For most examples we use unstructured meshes for which the elements 15are hexahedra (although this is not a requirement in libCEED). 16 17The physical coordinates are denoted by 18$\bm{x}=(x,y,z) \equiv (x_0,x_1,x_2) \in\Omega_e$, 19while the reference coordinates are represented as 20$\bm{X}=(X,Y,Z) \equiv (X_0,X_1,X_2) \in \textrm{I}=[-1,1]^3$ 21(for $d=3$). 22