Skip to content
Register Sign in Wishlist
Look Inside Finite Elements
eBook forthcoming

Finite Elements
Theory and Algorithms


Part of Cambridge IISc Series

  • Date Published: May 2017
  • availability: In stock
  • format: Hardback
  • isbn: 9781108415705

£ 54.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • Written in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.

    • Discusses the theories and algorithms of finite element methods in a coherent manner
    • The construction of finite elements on simplices, quadrilaterals and hexahedrals is discussed in detail
    • Explains object-oriented finite element algorithms and efficient implementation techniques
    Read more

    Reviews & endorsements

    'The book is written in a very traditional and straightforward style of theory and proof. The organization of the material makes it accessible for the reader to gain a foundational understanding of the topics … This book provides a readable, concise introduction to finite elements. Summing Up: Recommended.' S. L. Sullivan, CHOICE

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: May 2017
    • format: Hardback
    • isbn: 9781108415705
    • length: 216 pages
    • dimensions: 248 x 190 x 15 mm
    • weight: 0.47kg
    • availability: In stock
  • Table of Contents

    1. Sobolev spaces
    1.1. Banach and Hilbert spaces
    1.2. Weak derivatives
    1.3. Sobolev spaces
    2. Elliptic scalar problems
    2.1. A general elliptic problem of second order
    2.2. Weak solution
    2.3. Standard Galerkin method
    2.4. Abstract error estimate
    3. Finite element spaces
    3.1. Simplices and barycentric coordinates
    3.2. Simplicial finite elements and local spaces
    3.3. Construction of finite elements spaces
    3.4. The concept of mapped finite elements: affine mappings
    3.5. Finite elements on rectangular and brick meshes
    3.6. Mapped finite elements: general bijective mappings
    3.7. Mapped Qk finite elements
    3.8. Isoparametric finite elements
    3.9. Further examples of finite elements in C0 and C1
    4. Interpolation and discretization error
    4.1. Transformation formulas
    4.2. Affine equivalent finite elements
    4.3. Canonical interpolation
    4.4. Local and global interpolation error
    4.5. Improved L2 error estimates by duality
    4.6. Interpolation of less smooth functions
    5. Biharmonic equation
    5.1. Deflection of a thin clamped plate
    5.2. Weak formulation of the biharmonic equation
    5.3. Conforming finite element methods
    5.4. Nonconforming finite element methods
    6. Parabolic problems
    6.1. Conservation of energy
    6.2. A general parabolic problem of initial boundary value problems
    6.3. Weak formulation of initial boundary value problems
    6.4. Semidiscretization by finite elements
    6.5. Time discretization
    6.6. Finite elements for high-dimensional parabolic problems
    7. Systems in solid mechanics
    7.1. Linear elasticity
    7.2. Mindlin–Reissner plate
    8. Systems in fluid mechanics
    8.1. Conservation of mass and momentum
    8.2. Weak formulation of the Stokes problem
    8.3. Conforming discretizations of the Stokes problem
    8.4. Nonconforming discretizations of the Stokes problem
    8.5. The nonconforming Crouzeix–Raviart element
    8.6. Further inf–sup stable finite element pairs
    8.7. Equal order stabilized finite elements
    8.8. Navier–Stokes problem with mixed boundary conditions
    8.9. Time discretization and linearization of the Navier–Stokes problem
    9. Implementation of the finite element method
    9.1. Mesh handling and data structure
    9.2. Numerical integration
    9.3. Sparse matrix storage
    9.4. Assembling of system matrices and load vectors
    9.5. Inclusion of boundary conditions
    9.6. Solution of the algebraic systems
    9.7. Object-oriented C++ programming

  • Authors

    Sashikumaar Ganesan, Indian Institute of Science, Bangalore
    Sashikumaar Ganesan obtained his Ph.D. from Otto-von-Guericke-Universität Magdeburg, Germany 2006. He was Postdoctoral Fellow at Otto-von-Guericke-Universität Magdeburg, Germany (2006–08) and Research Associate (2008–09) at the Imperial College of Science, Technology and Medicine, London. He joined the Indian Institute of Science (IISc), Bangalore as Assistant Professor in 2011. He is currently heading a research group on Numerical Mathematics and Scientific Computing at Supercomputer Education and Research Centre, IISc, Bangalore. His areas of interest include numerical analysis, finite elements in fluid dynamics and high performance computing.

    Lutz Tobiska, Otto-von-Guericke-Universität Magdeburg, Germany
    Lutz Tobiska is Professor at the Institute for Analysis and Computational Mathematics, Otto-von-Guericke-Universität Magdeburg, Germany. He received his Ph.D. from the Technische Hochschule Magdeburg in 1977. He has published many articles in international journals. His areas of interest include finite elements in fluid dynamics, parallel algorithms, multigrid methods and adaptive methods for convection diffusion equations.

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.