Applied Mathematical Sciences

Least-Squares Finite Element Methods

Authors: Bochev, Pavel B., Gunzburger, Max D.

  • Puts least-squares finite element methods on a common mathematically sound foundation
  • Reviews strengths and weaknesses, successes and open problems of finite element methods
  • Appendices include results from functional analysis and standard finite theory
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  • ISBN 978-0-387-68922-7
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Hardcover $139.00
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Softcover $139.00
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  • ISBN 978-1-4419-2160-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engineers interested in either or both the theory and practice associated with the numerical solution of PDEs.

The first part looks at strengths and weaknesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems. Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods.

Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible discretizations for PDEs, multiphysics problems, and scientific computing.

Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics.

 

Reviews

From the reviews: “In the book under review, the authors give a unified and comprehensive treatment of least-squares finite element methods and discuss important implementation issues that are critical to their success in practice. … This book is valuable both for researchers and practitioners working in least-squares finite element methods. … In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods.” (Tsu-Fen Chen, Mathematical Reviews, Issue 2010 b)

Table of contents (16 chapters)

  • Vector Elliptic Equations

    Bochev, Pavel B. (et al.)

    Pages 1-40

  • The Navier–Stokes Equations

    Bochev, Pavel B. (et al.)

    Pages 1-55

  • Analysis Tools

    Bochev, Pavel B. (et al.)

    Pages 1-19

  • Parabolic Partial Differential Equations

    Bochev, Pavel B. (et al.)

    Pages 1-36

  • The Stokes Equations

    Bochev, Pavel B. (et al.)

    Pages 1-72

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-387-68922-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-0-387-30888-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4419-2160-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Least-Squares Finite Element Methods
Authors
Series Title
Applied Mathematical Sciences
Series Volume
166
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-68922-7
DOI
10.1007/b13382
Hardcover ISBN
978-0-387-30888-3
Softcover ISBN
978-1-4419-2160-4
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XXII, 660
Topics