A higher-order velocity post-processing for the Helmholtz equation

A macroelement post-processing recovery technique of the velocity field based on residuals of the equilibrium equation and irrotational conditions for the Helmholtz equation is proposed. The derivatives are recovered by solving local variational problems, that are based on the residuals aforementioned and involve superconvergent derivatives of the acoustical pressure field on special points. Improved accuracy for derivative finite element approximation is obtained with low computational cost and easy implementation. A number of comprehensive simulations is presented in order to show the main features of the proposed methodology.