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Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes

Ainsworth, Mark and Coyle, Joe (2001) Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Computer Methods in Applied Mechanics and Engineering, 190 (49-50). pp. 6709-6733.

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Abstract

We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Φ#169;) 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 Maxwell's equations that have singularities.