Implicit h type finite-element error estimator for the vector helmholtz equation

A dual-corrected, goal-oriented error estimator is presented. While existing methods employ p hierarchical basis functions for enriching the FE space for the dual problem, the present method uses hierarchichal h refinement, based on a hanging-variables framework. The paper emphasizes the importance of enriching the gradient subspace. Numerical results demonstrate that the proposed method restores optimal rates of convergence even in presence of singularities.