The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals, 7th Edition

The Finite Element Method: Its Basis and Fundamentals, 7th Edition,Olek Zienkiewicz,Robert Taylor,J.Z. Zhu,ISBN9781856176330

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The foremost introduction to FEM that no serious engineer concerned with finite elements should be without

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Key Features

  • A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development.
  • Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience.
  • Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.


The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.

This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover:

  • Weak forms
  • Variational forms
  • Multi-dimensional field problems
  • Automatic mesh generation
  • Plate bending and shells
  • Developments in meshless techniques

Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.


Mechanical, Civil and Electrical Engineers, applied mathematicians and computer aided engineering software developers

Olek Zienkiewicz

O. C. Zienkiewicz was one of the early pioneers of the finite element method and is internationally recognized as a leading figure in its development and wide-ranging application. He was awarded numerous honorary degrees, medals and awards over his career, including the Royal Medal of the Royal Society and Commander of the British Empire (CBE). He was a founding author of The Finite Element Method books and developed them through six editions over 40 years up to his death in 2009.

Affiliations and Expertise

Finite element method pioneer and former UNESCO Professor of Numerical Methods in Engineering, Barcelona, Spain

Robert Taylor

R. L. Taylor is Emeritus Professor of Engineering and Professor in the Graduate School, Department of Civil and Environmental Engineering at the University of California, Berkeley.

Affiliations and Expertise

Emeritus Professor of Engineering, University of California, Berkeley, USA.

J.Z. Zhu

J. Z. Zhu is a Senior Scientist at ProCAST, ESI Group, USA.

Affiliations and Expertise

Senior Scientist at ProCast Inc., ESI-Group North America, USA

The Finite Element Method: Its Basis and Fundamentals, 7th Edition

1. The Standard Discrete System and Origins of the Finite Element Method
2. Problems in Linear Elasticity and Fields
3. Weak Forms and Finite Element Approximation: 1-D Problems
4. Variational Forms and Finite Element Approximation: 1-D Problems
5. Field Problems: A Multidimensional Finite Element Method
6. Shape Functions, Derivatives, and Integration
7. Elasticity: Two- and Three-Dimensional Finite Elements
8. The Patch Test, Reduced Integration, and Nonconforming Elements
9. Mixed Formulation and Constraints: Complete Field Methods
10. Incompressible Problems, Mixed Methods and Other Procedures of Solution
11. Multidomain Mixed Approximations
12. The Time Dimension: Semi-Discretization of Field and Dynamic Problems
13. Plate Bending Approximation: Thin and Thick Plates
14. Shells as a Special Case of Three-Dimensional Analysis
15. Errors, Recovery Processes, and Error Estimates
16. Adaptive Finite Element Refinement
17. Automative Mesh Generation
18. Computer Procedures for Finite Element Analysis
A. Matrix Algebra
B. Some Vector Algebra
C. Tensor-Indicial Notation in the Approximation of Elasticity Problems
D. Solution of Simultaneous Linear Algebraic Equations
E. Triangle and Tetrahedron Integrals
F. Integration by Parts in Two or Three Dimensions (Green’s Theorem)
G. Solutions Exact at Nodes
H. Matrix Diagonalization or Lumping

Quotes and reviews

"...this is a book that you simply cannot afford to be without."--INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENGINEERING
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