  The Eilenberger-Larkin-Ovchinnikov-Eliashberg quasiclassical theory of
superconductivity is a powerful method enabling studies of a wide range of
equilibrium and non-equilibrium phenomena in conventional and unconventional
superconductors. We introduce here a finite element method, based on a
discontinuous Galerkin approach, to self-consistently solve the underlying
transport equations for general device geometries, arbitrary mean free path and
symmetry of the superconducting order parameter. We present results on i) the
influence of scalar impurity scattering on phase crystals in $d$-wave
superconducting grains at low temperatures and ii) the current flow and
focusing in $d$-wave superconducting weak links, modeling recent experimental
realizations of grooved high-temperature superconducting Dayem bridges. The
high adaptability of this finite element method for quasiclassical theory paves
the way for future investigations of superconducting devices and new physical
phenomena in unconventional superconductors.
