ABSTRACT
In this chapter, we will study the h and p mesh refinements. We begin with the construction of the extension operator corresponding to h refinement. The idea is fundamental in implementing the so-called constrained approximation in 2D and 3D codes. Next, we discuss the modification of order p for element middle nodes. This will naturally lead us to the idea of projection-based interpolation. We then return to the code and explain how the mesh modifications are realized in practice. We shall conclude the chapter with elementary interpolation error estimates and a discussion of the possible types of convergence and adaptivity.
