On the two dimension applications of high-order vector finite elements to the study of electromagnetic resonance

A set of hybrid vector-scalar finite elements for curved-triangle meshes is developed. These elements are applied to the study of electromagnetic resonance problems in which the variation in the field components along one coordinate is known in advance. The field component along this coordinate is modelled with polynomials of degree q. The other two field components are modelled with two dimension vector edge elements containing all irrotational functions up to polynomial degree m. Spurious modes are avoided only when q=m+1. The performance of these elements to order 4 is explored by applying them to some waveguides and axisymmetric cavities containing sharp edges, curved boundaries and/or uniaxially anisotropic materials