Interpolation Error Estimates for Edge Elements on Anisotropic Meshes

The classical error analysis for the Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in [18], optimal error estimates were obtained for the lowest order case, under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge singularities. In this paper, we prove optimal error estimates for the edge interpolation of any order under the maximum angle condition. We also obtain sharp stability results for that interpolation on appropriate families of elements.