On the influence of numerical integration on mixed finite element approximations of a Maxwell eigenvalue problem

Authors:
Wouter Hamelinck
Affiliations:
Research Group of Numerical Functional Analysis and Mathematical Modelling (NfaM2), Ghent University, Galglaan 2, 9000 Gent, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

The behaviour of electromagnetic resonances in cavities is modelled by a Maxwell eigenvalue problem (EVP). In the present work, we rewrite the corresponding variational problem, as it arises with a view to the application of a finite element method, in a mixed formulation. For the modelling of realistic problems the integrals occurring in this mixed formulation often cannot be evaluated exactly. We take into account the error arising from numerical quadrature and show convergence to the approximations using exact integration. Finally, some numerical results are presented.