Mass-Lumped Mixed Formulations and Edge Elements

Abstract

Solving the Maxwell equations by a finite element method is not so obvious since the appropriate functional framework for the solution is the space H(curl, Ω). Finite element functions in this space are required to have continuous tangential components at the interfaces of the elements. So, classical Lagrange finite elements described in the previous chapter, which are continuous, are not necessarily best for the approximation of such spaces. The appropriate finite element space was introduced by Nédélec in the 1980s [92, 93] and the elements of this space are now called edge elements. In this section and in the following, we shall study quadrilateral and hexahedral edge elements with mass-lumping. More precisely, this section will deal with the so-called first family of Nédélec’s (or edge) elements [92] on orthogonal meshes.