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The Finite Element Method: Theory, Implementation, and Applications

  • Textbook
  • © 2013

Overview

Authors:
  1. Mats G. Larson

    1. , Department of Mathematics, Umeå University, Umea, Sweden

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  2. Fredrik Bengzon

    1. , Department of Mathematics, Umeå University, Umea, Sweden

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    You can also search for this author in PubMed   Google Scholar

  • 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
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  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
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Keywords

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

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