Introduction to Finite Elements Methods by Hans Langtangen
Introduction to Finite Elements Methods - Table of Contents
- 1. Approximation of Vectors
- 2. Approximation of Functions
- 3. Finite Element Basis Functions
- 4. Implementation
- 5. Comparison of Finite Element & Finite Difference Approximation
- 6. Generalized Element Concept
- 7. Numerical Integration
- 8. Approximation of Functions in 2D
- 9. Finite Elements in 2D and 3D
- 10. Exercises
- 11. Basic Principles for Approximating Differential Equations
- 12. Examples on Variational Formulations
- 13. Computing with Finite Elements
- 14. Boundary Conditions: Specified Nonzero Value
- 15. Boundary Conditions: Specified Derivative
- 16. Implementation
- 17. Variational Formulations in 2D and 3D
- 18. Summary
- 19. Time-Dependent Problems
- 20. Systems of Differential Equations
- 21. Exercises
What You Will Learn in Introduction to Finite Elements Methods
Introduction to Finite Element Methods by Hans Petter Langtangen and Kent-Andre Mardal is an authoritative open-access textbook designed for upper-level undergraduate and graduate students in computational engineering, applied mathematics, and computer science. Serving as an essential study guide, this volume provides a robust framework for finite element analysis and computational PDE problem solving practice.
The textbook systematically covers vector space function approximations, the least squares method, the Galerkin projection method, 1D/2D/3D mesh generation, reference element mappings, variational formulations, time-dependent PDEs, and nonlinear differential systems. By integrating mathematical derivations with Python and FEniCS implementations, Langtangen enables readers to execute complex element matrix assembly and numerical boundary value solutions with precision.
Treasured globally by engineers and computational scientists for its programming-oriented approach and intuitive physical examples, this modern monograph remains an indispensable self-study guide. Langtangen’s practical methodology equips learners with vital analytical techniques required for mastering modern finite element modeling and simulation principles.
Book Details & Specifications
Title:
Introduction to Finite Elements Methods by Hans Langtangen
Publisher:
Norwegian Centre of ExcellenceExternal Educational Resource (author-provided)
Year:
2013
Pages:
171
Type:
PDF
Language:
English
ISBN-10 #:
0495668257
ISBN-13 #:
978-0495668251
License:
External Educational Resource
Amazon:
Amazon
About the Author: Hans Petter Langtangen
The author Hans Petter Langtangen
(1962–2016) was a distinguished Professor of Computer Science at the University of Oslo and Director of the Center for Biomedical Computing at Simula Research Laboratory, world-renowned for his pioneering work in scientific computing and open-source software like FEniCS.
His classic open textbooks stand as foundational finite element methods, computational PDEs, and scientific Python programming study guides.
Read or Downloadable Introduction to Finite Elements Methods
Free Numerical Analysis Books PDF | Download Computational Guides