The ?nite element method is the most powerful general-purpose technique for comput?ing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the ?nite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. It includes a carefully documented collection of MATLAB (R) programs implementing the ideas presented in the book. Readers will bene?t from a careful explanation of data structures and speci?c coding strategies and will learn how to write a ?nite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways to learn more about programming ?nite elements.
Mark S. Gockenbach is a Professor of Mathematical Sciences at Michigan Technological University. His research interests include inverse problems, computational optimization, and mathematical software. His first book, Partial Differential Equations: Analytical and Numerical Methods, was published by SIAM in 2002.
Preface Part I: The Basic Framework for Stationary Problems. Chapter 1: Some Model PDEs Chapter 2: The weak form of a BVP Chapter 3: The Galerkin method Chapter 4: Piecewise polynomials and the finite element method Chapter 5: Convergence of the finite element method Part II Data Structures and Implementation. Chapter 6: The mesh data structure Chapter 7: Programming the finite element method: Linear Lagrange triangles Chapter 8: Lagrange triangles of arbitrary degree Chapter 9: The finite element method for general BVPs Part III: Solving the Finite Element Equations. Chapter 10: Direct solution of sparse linear systems Chapter 11: Iterative methods: Conjugate gradients Chapter 12: The classical stationary iterations Chapter 13: The multigrid method Part IV: Adaptive Methods. Chapter 14: Adaptive mesh generation Chapter 15: Error estimators and indicators Bibliography Index.
'Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent.' Anthony Kearsley, National Institute of Standards and Technology
