In this paper, numerical and implementation aspects of the phase-field crystal model with elastic interactions are addressed. This model leads to a time-dependent, sixth-order system of differential equations which yields a continuous density field, from which individual atom positions can be extracted and tracked in time. We solve the system using high-order finite elements, and reconstruct the elastic properties of the crystal from the atomic displacements with a meshless interpolation scheme. Numerical simulations are performed of benchmark experiments, which include deformation and dislocation dynamics.