Finite Element Methods: A Practical Guide (Mathematical Engineering)

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students. Front Matter....Pages i-xi An Overview of the Finite Element Method....Pages 1-4 A First Example....Pages 5-23 Linear Boundary Value Problems....Pages 25-53 Higher Order Basis Functions....Pages 55-80 Nonlinear Boundary Value Problems....Pages 81-101 Systems of Ordinary Differential Equations....Pages 103-118 Linear Elliptic Partial Differential Equations....Pages 119-141 More General Elliptic Problems....Pages 143-160 Quadrilateral Elements....Pages 161-173 Higher Order Basis Functions....Pages 175-188 Nonlinear Elliptic Partial Differential Equations....Pages 189-196 Systems of Elliptic Equations....Pages 197-202 Parabolic Partial Differential Equations....Pages 203-209 Back Matter....Pages 211-232