Mesh orientation

Abstract

Orienting the edges and the faces of a mesh is crucial when working with finite elements whose degrees of freedom invoke normal or tangential components of vector fields. This notion is also important when working with high-order scalar-valued finite elements, since it helps to enumerate consistently all the degrees of freedom in the mesh cells sharing an edge or a face with other mesh cells. In this chapter, we focus on matching meshes, and we assume that the meshes are affine. We first explain how to orient meshes. Then we introduce the important notion of generation-compatible orientation. Finally, we investigate whether simplicial, quadrangular, and hexahedral meshes can be equipped with a generation-compatible orientation.