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A systematic introduction to partial differential
equations and modern finite element methods for their efficient numerical solution
Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM.
A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations.
The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM.
Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science.
Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.
- Sales Rank: #3454974 in Books
- Published on: 2005-11-25
- Original language: English
- Number of items: 1
- Dimensions: 9.35" h x 1.17" w x 6.42" l, 2.35 pounds
- Binding: Hardcover
- 504 pages
Review
"This well-written book discusses the modern methods of partial differential equations and the finite element methods…recommended." (CHOICE, July 2006)
From the Back Cover
A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution
Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM.
A solid introduction to the theory of PDEs and FEM contained in Chapters 1–4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations.
The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM.
Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science.
Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.
About the Author
PAVEL SOLÍN, PhD, is Associate Professor in the Department of Mathematical Sciences at The University of Texas at El Paso. Prior to this appointment, Dr. Solin was a postdoctoral research associate at the Johannes Kepler University (Linz, Austria), The University of Texas at Austin, and Rice University (Houston, Texas). He received his PhD from the Charles University in Prague, Czech Republic, in 1999. Dr. Sol?n is a coauthor of the monograph Higher-Order Finite Element Methods.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Very purist graduate math book
By Ssound
First let me start by stating that im an engineer doing graduate studies, and im not the type of person who discredits a book just because it is hard or because I couldnt understand it, if this book were catalogued as a pure mathematics book, then I would be completely out of place to misjudge it, however the book states in the back cover that it is meant for engineers and scientists therefore I will rate it from that perspective.
To start, I guess that the professor teaching my class thought it would be funny to assign this as the text book for the course, a textbook which is clearly for mathematicians (contrary to what the book states) to a classroom full of engineers. The book does include applications of the method to engineering/science topics such as mechanics, electromagnetism, etc.. but the complexity on how the material is presented clouds any useful information.
The back cover states: "...this student tested publication is geared to upper level undergraduates and graduate students in all disciplines of computational engineering and science, its also a practical problem-solving reference for researchers, engineers and physicists" , I disagree... first of all the book is anything but practical, its a rigurous book full of lemma's, theorem's and proofs, the notation alone will make you pull your hairs out, everything is written in convoluted mathematical notation, something as simple as explaining how to tell the difference between a hyperbolic or parabolic equation is full of fussiness and extreme mathematical jargon. Now dont get me wrong, it is expected that a student at this level should posses a good mathematical background, but the amount of pre-requisites you need to follow this text is out of what may be considered standard engineering curricula.
To give you a better perspective, the book starts by strongly suggesting the student to read the appendix on functional analysis before reading the main chapters, it just turns out that the appendix is almost 120 pages long, however you start reading the appendix and you realize that you need to understand other things such as variational calculus, Hilbert and Sobolev spaces, and lots of things before even reading the appendix, soon enough, if you are like me you'll realize that you cant read book, at least you wont understand it, everytime I tried to read it I felt like a 5 year old trying to read a calculus book, I really struggle to read even 3 pages, not saying im too dumb to read it, I just dont have the sufficient mathematical requirements, I either need a second major in math, or to take 5-6 courses before reading this book, I just dont have the time nor the interest in that, and apparently everyone else in my class feels the same way.
This book is simply not for engineers or physicists, let me give you an example using electromagnetics , and let me apollogize for the lack of quality mathematical fonts but I'll try to quote part of the book (page 4):
"Let the function ''C(') represent the electric charge density in some open bouded set ' c R. If the ' permitivity is constant in ' the distribution of the electric potential ' in 'is governed by the Poisson equation."
Seriously, when in your life have you seen an engineer or phycisist state a problem in such way?? in fact when have you read any electromagnetics book stating a problem in such way?, this is clearly a mathematician trying to state a physics problem the way mathematicians state mathematical problems. This example should give you a 'feel' of the way this book is presented.
This book is going to my shelf, perhaps I will re-open it in 10 years and be able to read more than 3 pages, as of now, I have 4 other books which cover partial differential equations and the finite element method which I'll use to pass the course, some of the books are also complex but very readable. The books im refering to are the following: "Numerical Solution of Partial Differential Equations by the Finite Element Method" by Johnson, "Finite element method" by Reddy, "The finite element method" by Hughes and "Applied finite element analysis" by Segerlind.
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