Space-time enriched finite elements for transient wave problems

We investigate a generalised finite element method for the time-dependent wave equation based on enriching the approximation space with travelling plane waves. Our approach is based on a first-order discontinuous Galerkin formulation for the wave equation, discretised with continuous elements in space and discontinuous elements in time. Enrichment in space and time allows us to circumvent the limitations due to the small time steps required for time-independent enrichments. We obtain good approximation for coarse spatial meshes and large time steps, with a corresponding reduction in computational effort. Numerical results indicate the advantages of the proposed approach and investigate the attained accuracy of our scheme as the number of enrichment functions are increased.