${{{\varvec{H}}(\mathrm{curl})}}$ finite elements

Abstract

The goal of this chapter is to construct vector-valued finite elements to approximate fields with integrable curl. The finite elements introduced in this chapter can be used, e.g., to approximate (simplified forms of) Maxwell’s equations which constitute a fundamental model in electromagnetism. The focus here is on defining a reference element and generating finite elements on the mesh cells. The interpolation error analysis is done in Chapters 16 and 17. We detail the construction for the simplicial Nédélec finite elements of the first kind. Some alternative elements are outlined at the end of the chapter.