We extend the work of Marazzato et al. (2020) on elastodynamics to the treatment of contact. To that end, we propose adequate handling of boundary conditions, either through the resolution of local problems on each of the face displacement unknowns or through interpolation from nearest neighbours. Adapting the time-integration strategy adopted in Marazzato et al. (2019), it is possible to conserve both momentum and a pseudoenergy exactly. Numerical results are presented to illustrate the accuracy of contact treatment and the energy conservation of the system.