A discontinuous finite element method for the helmholtz equation

We present a novel approach to improving computational acoustics. The standard finite element polynomial field is enriched by a field of plane waves at predetermined directions. The enrichment is added to the polynomial field. Consequently, this field is not continuous across element boundaries ab initio, and continuity is enforced weakly by Lagrange multipliers. In the implementation presented herein, an underlying bilinear polynomial field is enriched by four plane waves aligned with the axes, with continuity enforced by piecewise constants along element sides. Dispersion analyses demonstrate the accuracy of the formulation. The good dispersion properties are confirmed by accurate solutions on numerical tests, which also indicate adequate conditioning of the formulation. The present method is a specialization to acoustics of the discontinuous enrichment method, a general approach that is currently under development.