Studies of the discontinuous enrichment method for two-dimensional acoustics

The discontinuous enrichment method (DEM) for boundary-value problems governed by the Helmholtz equation is reviewed. Quadrilateral and triangular DEM elements for acoustics are considered. Conditioning considerations indicate preferred representations of the oscillatory basis functions. Dispersion properties are used to rate the performance of different element configurations. Numerical results indicate that high-order DEM elements exhibit little pollution. The dispersion and the numerical results are in a good agreement. The proposed configurations of DEM elements become more competitive as the enrichment and Lagrange multipliers are enhanced.