Finite Element Methods

In this chapter we outline the finite element formulations that are essential to solve the partial differential equations of nonlinear elasticity, transient mass transport, and of the phase field formulations presented in Chaps. 2 and 3 . As in those chapters the treatment is directed at the practitioner who already has some familiarity with the finite element method and is seeking some insight to its use in the chapters that follow. It does not aim to be a primary source to learn the finite element method. We direct the reader to the classical textbook by Hughes (The finite element method: linear static and dynamic finite element analysis. Courier Corporation, 2012) for a broad as well as deep treatment of the mathematical foundations and implementation of the finite element method for transient mass transport (as well as of linearized elasticity).