Edge elements on anisotropic meshes and approximation of the Maxwell equations

摘要

This paper deals with some edge element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived for all these types of elements and for functions from classical and weighted Sobolev spaces. As a particular application, the numerical approximation of the Maxwell equations in domains with edges is investigated using Nedelec's edge elements, where anisotropic finite element meshes are appropriate. Some anisotropic regularity results of the solutions of Maxwell equations on such domains are proved. Some numerical tests are described and inverse estimates are established, both showing that our theoretical orders of convergence are optimal. [References: 38]