1*bcb2dfaeSJed Brown(common-notation)= 2*bcb2dfaeSJed Brown 3*bcb2dfaeSJed Brown# Common notation 4*bcb2dfaeSJed Brown 5*bcb2dfaeSJed BrownFor most of our examples, the spatial discretization 6*bcb2dfaeSJed Brownuses high-order finite elements/spectral elements, namely, the high-order Lagrange 7*bcb2dfaeSJed Brownpolynomials defined over $P$ non-uniformly spaced nodes, the 8*bcb2dfaeSJed BrownGauss-Legendre-Lobatto (GLL) points, and quadrature points $\{q_i\}_{i=1}^Q$, with 9*bcb2dfaeSJed Browncorresponding weights $\{w_i\}_{i=1}^Q$ (typically the ones given by Gauss 10*bcb2dfaeSJed Brownor Gauss-Lobatto quadratures, that are built in the library). 11*bcb2dfaeSJed Brown 12*bcb2dfaeSJed BrownWe discretize the domain, $\Omega \subset \mathbb{R}^d$ (with $d=1,2,3$, 13*bcb2dfaeSJed Browntypically) by letting $\Omega = \bigcup_{e=1}^{N_e}\Omega_e$, with $N_e$ 14*bcb2dfaeSJed Browndisjoint elements. For most examples we use unstructured meshes for which the elements 15*bcb2dfaeSJed Brownare hexahedra (although this is not a requirement in libCEED). 16*bcb2dfaeSJed Brown 17*bcb2dfaeSJed BrownThe physical coordinates are denoted by 18*bcb2dfaeSJed Brown$\bm{x}=(x,y,z) \equiv (x_0,x_1,x_2) \in\Omega_e$, 19*bcb2dfaeSJed Brownwhile the reference coordinates are represented as 20*bcb2dfaeSJed Brown$\bm{X}=(X,Y,Z) \equiv (X_0,X_1,X_2) \in \textrm{I}=[-1,1]^3$ 21*bcb2dfaeSJed Brown(for $d=3$). 22