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  • Textbook
  • © 2013

The Finite Element Method: Theory, Implementation, and Applications

  • Introduction to finite elements only based on calculus and linear algebra
  • Covers theory, implementation and applications. Focus on basic mathematical principles and consequent use of the same approach in different applications
  • Matlab programs included
  • Wide range of applications including solid mechanics, electromagnetics, and fluid mechanics
  • Covers modern topics such as adaptivity based on duality arguments?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 10)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvii
  2. Piecewise Polynomial Approximation in 1D

    • Mats G. Larson, Fredrik Bengzon
    Pages 1-22
  3. The Finite Element Method in 1D

    • Mats G. Larson, Fredrik Bengzon
    Pages 23-44
  4. Piecewise Polynomial Approximation in 2D

    • Mats G. Larson, Fredrik Bengzon
    Pages 45-69
  5. The Finite Element Method in 2D

    • Mats G. Larson, Fredrik Bengzon
    Pages 71-111
  6. Time-Dependent Problems

    • Mats G. Larson, Fredrik Bengzon
    Pages 113-142
  7. Solving Large Sparse Linear Systems

    • Mats G. Larson, Fredrik Bengzon
    Pages 143-176
  8. Abstract Finite Element Analysis

    • Mats G. Larson, Fredrik Bengzon
    Pages 177-201
  9. The Finite Element

    • Mats G. Larson, Fredrik Bengzon
    Pages 203-223
  10. Non-linear Problems

    • Mats G. Larson, Fredrik Bengzon
    Pages 225-239
  11. Transport Problems

    • Mats G. Larson, Fredrik Bengzon
    Pages 241-256
  12. Solid Mechanics

    • Mats G. Larson, Fredrik Bengzon
    Pages 257-287
  13. Fluid Mechanics

    • Mats G. Larson, Fredrik Bengzon
    Pages 289-325
  14. Electromagnetics

    • Mats G. Larson, Fredrik Bengzon
    Pages 327-354
  15. Discontinuous Galerkin Methods

    • Mats G. Larson, Fredrik Bengzon
    Pages 355-372
  16. Back Matter

    Pages 373-385

About this book

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​    

Reviews

From the reviews:

“The authors give an introduction to the finite element method as a general computational method for solving partial differential equations (PDEs) approximately. … The book should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed.” (Răzvan Răducanu, Zentralblatt MATH, Vol. 1263, 2013)

Authors and Affiliations

  • , Department of Mathematics, Umeå University, Umea, Sweden

    Mats G. Larson, Fredrik Bengzon

Bibliographic Information

Buy it now

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access