Whiteley J. Finite Element Methods: A Practical Guide

Springer International Publishing AG, 2017. — 236 p. — (Mathematical Engineering) — ISBN: 331949970XThis book has evolved from courses on the finite element method that have been taught as part of several graduate programmes at the University of Oxford. These courses have all focused on the practical application of the finite element method. A typical course would begin with a specific class of differential equations being written down. The course would then provide students with all the detail that is required to develop a computational implementation of the finite element method for this class of differential equations. This approach requires the following topics to be addressed: (i) derivation of the weak formulation of a differential equation; (ii) discretisation of the domain on which the differential equation is defined into elements; (iii) specification of suitable basis functions; (iv) derivation of a system of algebraic equations that is derived from the finite element formulation of the differential equation; (v) solution of this system of algebraic equations; and (perhaps most importantly) (vi) the practical implementation of all steps. This book is written in the spirit in which these courses have been taught. Mathematical rigour is certainly needed when discussing some of these topics, such as the use of Sobolev spaces when deriving the weak formulation of a differential equation. The focus, however, is on the practical implementation of the finite element method for a given differential equation.An Overview of the Finite Element Method
A First Example
Linear Boundary Value Problems
Higher Order Basis Functions
Nonlinear Boundary Value Problems
Systems of Ordinary Differential Equations
Linear Elliptic Partial Differential Equations
More General Elliptic Problems
Quadrilateral Elements
Higher Order Basis Functions
Nonlinear Elliptic Partial Differential Equations
Systems of Elliptic Equations
Parabolic Partial Differential Equations
Appendixes
Methods for Solving Linear and Nonlinear Systems of Algebraic Equations
Vector Calculus