The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime

The discontinuous enrichment method (DEM) is specified and developed for the solution of twodimensional elastic wave propagation problems in the frequency domain. The classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions. The continuity of the solution across the element interfaces is weakly enforced by suitable Lagrange multipliers. Higher-order rectangular DEM elements are constructed and benchmarked against the standard higher-order polynomial Galerkin elements for two-dimensional problems in the medium frequency regime. In general, it is found that for such applications, DEM can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom. This highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium.