The most important application of the finite element method is the numerical solution of elliptical partial differential equations. This is covered in depth in this book. It is a textbook for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite elements for engineering or mathematics applications.
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Book Description
Editorial Reviews
Review
'This is a well-written book on the mathematical foundation of the finite element method which should appeal to graduate mathematicians and researchers in numerical methods and theoretical mechanics. The coveraGE OF THE MATHEMATICAL THEORIES USED IN THE FINITE ELEMENT FORMULATION IS COMPREHENSIVE.' A. A. Becker, Journal of Mechanical Engineering Science
' ... this is an excellent book that is appealing to both mathematicians and engineers'. N Herrmann, Zentralblatt für Mathematik und ihre Grenzgebiete
'The book is well suited as a student's textbook in an introductory finite element class, but also for the lecturer himself for designing such courses ... Readers with interest in time dependent problems, in the treatment of nonlinear elliptic partial differential equations, or those which are more interested in practical implementation, obtain in this book a solid theoretical foundation. The book is highly recommended.' H. Blum, University of Dortmund
' ... this is an excellent book that is appealing to both mathematicians and engineers'. N Herrmann, Zentralblatt für Mathematik und ihre Grenzgebiete
'The book is well suited as a student's textbook in an introductory finite element class, but also for the lecturer himself for designing such courses ... Readers with interest in time dependent problems, in the treatment of nonlinear elliptic partial differential equations, or those which are more interested in practical implementation, obtain in this book a solid theoretical foundation. The book is highly recommended.' H. Blum, University of Dortmund
Language Notes
Text: English (translation)
Original Language: German --This text refers to an out of print or unavailable edition of this title.
Original Language: German --This text refers to an out of print or unavailable edition of this title.
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Most Helpful Customer Reviews
2 of 2 people found the following review helpful:
4.0 out of 5 stars
A decent introduction to theory and methods for FEM,
This review is from: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics (Paperback)
I would say I mostly agree with the previous reviewer. The description is pretty clear, despite being a translation, and it has actually proven useful to me during my time in grad school. One minor complaint I have is that some of the proofs he gives are not as clear as I would like them to be. Specifically, I am talking about the sections dealing with the INF-SUP condition. It seems that everyone who writes an FEM book either skirts this whole issue of the INF-SUP condition (which is what a lot of engineering texts do), or they just copy the 'standard' proofs, which suck. But other than that, this is a useful book to have.
4 of 5 people found the following review helpful:
4.0 out of 5 stars
A Good Book To Learn Finite Elements From,
By
This review is from: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics (Paperback)
I recently read this book as part of an advanced numerical analysis class in grad school. I found it to be well written and easy to read. It was useful to me in learning about finite elements from both an abstract and practical perspective. I would recommend it to anyone familiar with the concept of a weak solution to an elliptic partial differential equation and with some experience with numerical linear algebra.This book could have been improved by including some code or pseudo-code to help get novices started. This is not too severe of a drawback since the text is so well written that the reader should be able to implement many of the ideas without any other training in this area.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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solid mechanics, posteriori error estimates, approximation properties, space decomposition, characterization theorem, convergence theorem, multigrid analysis, congruent subtriangles, nonconforming methods, affine families, saddle point problem, classical iterative methods, bilinear quadrilateral elements, affine family, conforming finite elements, nonconforming elements, minimal residual method, residual estimators, finite element spaces, data oscillation, inverse estimate, nodal basis, discrete maximum principle, trace theorem, linear elasticity theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Finite Elements, The Kirchhoff Plate, The Mindlin-Reissner Plate, Simple Boundary Approximation, The Neumann Boundary-Value Problem, The Conjugate Gradient Method, Variational Formulation of Elliptic Boundary-Value Problems, Further Tools, Existence Theorem, Functional Analysis, Computational Considerations, Nonlinear Problems, Finite Difference Methods, Multigrid Methods New!
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solid mechanics, posteriori error estimates, approximation properties, space decomposition, characterization theorem, convergence theorem, multigrid analysis, congruent subtriangles, nonconforming methods, affine families, saddle point problem, classical iterative methods, bilinear quadrilateral elements, affine family, conforming finite elements, nonconforming elements, minimal residual method, residual estimators, finite element spaces, data oscillation, inverse estimate, nodal basis, discrete maximum principle, trace theorem, linear elasticity theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Finite Elements, The Kirchhoff Plate, The Mindlin-Reissner Plate, Simple Boundary Approximation, The Neumann Boundary-Value Problem, The Conjugate Gradient Method, Variational Formulation of Elliptic Boundary-Value Problems, Further Tools, Existence Theorem, Functional Analysis, Computational Considerations, Nonlinear Problems, Finite Difference Methods, Multigrid Methods New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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