Hierarchic hp-edge element families for Maxwellʹs equations on hybrid quadrilateral/triangular meshes Original Research Article

We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Ω) suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non-uniform order polynomial approximation. We investigate the conditioning and dispersive behaviour of the elements. In addition, numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time-harmonic Maxwellʹs equations that have singularities.