  The Lagrange-mesh method is an approximate variational method taking the form
of equations on a grid because of the use of a Gauss quadrature approximation.
With a basis of Lagrange functions involving associated Laguerre polynomials
related to the Gauss quadrature, the method is applied to the Dirac equation.
The potential may possess a $1/r$ singularity. For hydrogenic atoms,
numerically exact energies and wave functions are obtained with small numbers
$n+1$ of mesh points, where $n$ is the principal quantum number. Numerically
exact mean values of powers $-2$ to 3 of the radial coordinate $r$ can also be
obtained with $n+2$ mesh points. For the Yukawa potential, a 15-digit agreement
with benchmark energies of the literature is obtained with 50 mesh points or
less.
