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We study the effects of numerical quadrature rules on error convergence rateswhen solving Maxwell-type variational problems via the curl-conforming or edgefinite element method. A complete {\em a priori} error analysis for the case ofbounded polygonal and curved domains with non-homogeneous coefficients isprovided. We detail sufficient conditions with respect to mesh refinement andprecision for the quadrature rules so as to guarantee convergence ratesfollowing that of exact numerical integration. On curved domains, we isolatethe error contribution to numerical quadrature rules.

The effect of quadrature rules on finite element solutions of Maxwell  variational problems. Consistency estimates on meshes with straight and  curved elements