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 and Finite Difference Approximation
6. A 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 is a beginner-friendly guide that explains how "finite element methods", "numerical modeling", "engineering simulation", "partial differential equations", and "scientific computing" are used to solve real-world problems. The book starts with simple ideas and gradually builds understanding, making complex mathematics easier to follow. Clear explanations help readers see how large physical problems can be divided into smaller, manageable pieces called elements.
A key strength of the book is its practical approach. Langtangen connects theory with implementation by using programming examples, mainly in Python. This hands-on style allows readers to experiment, visualize results, and understand how equations turn into working simulations. The book focuses on problem-solving rather than heavy proofs, which makes it ideal for students and engineers who want usable knowledge.
Overall, this book bridges the gap between mathematical theory and real applications. It is well suited for self-study, university courses, and professionals entering computational science. By combining clear explanations, practical coding, and real examples, the book builds strong confidence in applying the finite element method to science and engineering challenges.
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
was a respected Norwegian scientist and educator known for his contributions to "scientific computing", "finite element methods", "numerical analysis", "computational modeling", and "Python programming". He served as a professor at the University of Oslo and played a key role at the Simula Research Laboratory, where he helped advance modern computational science education. He authored influential textbooks that combined clear theory with practical coding examples, making complex numerical methods easier to learn. Langtangen was also an active researcher, mentor, and journal editor, remembered for his passion for teaching and his lasting impact on engineering and scientific computing education.
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