ABSTRACT
We discuss the fundamentals of hp finite elements in two space dimensions. We begin by partitioning domain into finite elements. The 2D elements have shapes of triangles or quadrilaterals (quads), possibly with curvilinear edges. In this chapter, we shall focus on regular meshes. A mesh, consisting possibly of both triangles and quads is called regular, if the intersection of any two elements in the mesh is either empty, reduces to a single vertex, or consists of a whole common edge shared by the elements. The case of the so-called irregular meshes with “hanging nodes” arising naturally from h refinements will be discussed in the next chapters.
