An Introduction to the p- and hp-Versions of the Finite Element Method

Abstract

The various methods described in this monograph for the computation of eigenpairs and GFIF/GSIFs cannot in general be carried out by means of analytical techniques; thus they require the use of numerical methods. We use the p_version of the FE method as the machinery for obtaining the required quantities, therefore, this chapter provides a brief introduction to these methods, their main features and characteristics. Readers interested in the mathematical aspects of p_ and hp_FEMs are encouraged to consult Schwab’s book [157] whereas details on the applicative aspects of p_ and spectral FE methods are well documented in Karniadakis and Scherwin’s book [92] and Szab´o and Babu?ska’s book [178].