Best Reference Books – Mathematical Theory of Finite Elements

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We have compiled the list of Top 10 Best Reference Books on Mathematical Theory of Finite Elements subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Mathematical Theory of Finite Elements along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Mathematical Theory of Finite Elements subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Mathematical Theory of Finite Elements" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “The Mathematical Theory of Finite Element Methods” by K E Brenner and R Scott

“The Mathematical Theory of Finite Element Methods” Book Review: This book has rigorous and thorough mathematical introduction to the foundations of the subject with a clear and concise treatment of modern fast solution technique. This book helps in developing the fundamental mathematical theory of the finite element method, along with the most widely used technique for engineering design and analysis. Piecewise exercise has been added in this book. The initial chapters provide an introduction to the whole subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. This subsequent topic covered in this book are mixed methods with applications to elasticity and fluid mechanics, iterated penalty and augmented Lagrangian methods, nonconforming and isoparametric methods, numerical integration and interior penalty methods. This book is useful to mathematicians as well as engineers & physical scientists. This book can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory.

2. “The Finite Element Methods for Elliptic Problems” by P G Ciarlet

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“The Finite Element Methods for Elliptic Problems” Book Review: This book gives a precise and concise introduction to the topic and is written in simple & student friendly language. This book is there to analyze the basic mathematical aspect of Element Method and also as current research to the topic. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses and is useful for gate aspirants. This book is useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. It also serves as a textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty. This also covers the new and latest concepts on the topic.

3. “Numerical Solutions of Partial Differential Equations by Finite Element Methods” by C Johnson

“Numerical Solutions of Partial Differential Equations by Finite Element Methods” Book Review: This book is a brief introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. This book is for advanced undergraduate & graduate courses and gives a clear connection between the topic with applications along with numerous examples from a variety of science- and engineering-related specialties for better view on the topic . This book has all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Topics included here are finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. This book serves well to the topic.

4. “An Introduction to the Mathematical Theory of Finite Elements” by J T Oden and J N Reddy

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“An Introduction to the Mathematical Theory of Finite Elements” Book Review: This book goes through fundamentals and will teach you the foundation aspects of the topic. It offers logical, easy to access demonstrations of the use of the techniques in developing the foundations of the theory of finite element approximations. The book covers topics like the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. This book is designed with self contained texts such that it will be effective for students from diverse educational background. This book has solved examples and has detailed proofs of the theorem of the topic and has numerous examples for clear understanding. This book is helpful to anyone who wants a firm grip on the topic.

5. “Finite Element Analysis Theory and Application with ANSYS” by Saeed Moaveni

“Finite Element Analysis Theory and Application with ANSYS” Book Review: This book has a well precise and understandable context on the topic and explores all the aspects of the topic along with using the context effectively and efficiently. This book presents well the theory of finite element analysis along with exploring its application as a design or modeling tool, with explaining in detail how to use ANSYS intelligently and effectively. This book will helps student by presenting the Theory of Finite Element Analysis for their understanding and also explains how to use ANSYS efficiently, it also has open designed problems to help students so that they can apply the concept in a better way. It has simple finite problems along with new problems for the more logical aspect of the topic. This book is a useful reference for mechanical, civil and environmental engineers.

6. “Advanced Topics in Finite Element Analysis of Structures: With Mathematica and MATLAB” by M Asghar Bhatti

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“Advanced Topics in Finite Element Analysis of Structures: With Mathematica and MATLAB” Book Review: This book helps in developing the fundamental mathematical theory of the finite element method, along with the most widely used technique for engineering design and analysis. This book uses a unique and consistently weighted residual approach to present advanced topics such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book follows a hands on approach on the topic through integrated mathematical exercises and MATLAB exercises. It also has exercises of varying nature for good practice and understanding as well along with a very practical approach which enhances the creative part of the reader. This book will be very useful for who wants a deep dive of the topic.

7. “The Finite Element Method in Electromagnetics” by Jian-Ming Jin

“The Finite Element Method in Electromagnetics” Book Review: This book explains the method’s processes and techniques in careful, meticulous prose and covers not only the finite element method theory, but also its latest developments and applications that gives engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Its essential and comprehensive text focuses on a wider range of applications of the topic including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics, along with the finite element analysis of wave propagation, scattering, and radiation in periodic structures, the time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena. This book has a great sum of examples and is ideal for engineering students as well as professionals in this field.

8. “Finite Element Analysis: Theory and Application with ANSYS” by Saeed Moaveni

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“Finite Element Analysis Theory and Application with ANSYS” Book Review: This book has a well precise and understandable context on the topic and explores all the aspects of the topic along with using the context effectively and efficiently. This book presents well the theory of finite element analysis along with exploring its application as a design or modeling tool, with explaining in detail how to use ANSYS intelligently and effectively. This book will helps student by presenting the Theory of Finite Element Analysis for their understanding and also explains how to use ANSYS efficiently, it also has open designed problems to help students so that they can apply the concept in a better way. It has simple finite problems along with new problems for the more logical aspect of the topic. This book is a useful reference for mechanical, civil and environmental engineers.

9. “Programming the Finite Element Method” by I M Smith and D V Griffiths

“Programming the Finite Element Method” Book Review: This book has a programming oriented approach for the context. This book gives the reader learning how to develop computer programs to solve specific engineering problems using the finite element method. This book includes programs, subroutine & provides topics like advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary conditions, and interfaces to third party tools such as ParaView, METIS and ARPACK. This book has a wide range of problems and exercises that are presented including topics like structural analysis, elasticity and plasticity, construction processes in geomechanics, uncoupled and coupled steady and transient fluid flow and linear and nonlinear solid dynamics. This book is aimed at all professional peoples and students who are into programming and is ideal for undergraduate and postgraduate students in civil and mechanical engineering, applied mathematics and numerical analysis, and is also a comprehensive reference for practitioners.

10. “Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics” by Dietrich Braess

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“Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics” Book Review: This book is fully updated on the context and features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and is explained to include many more nonstandard applications. This book discusses the subject very comprehensively. It has solved numerical problems which gives a better understanding of the topic which includes numerical solution of elliptic partial differential equations, application of finite elements. The graduate students who do not have any particular background in differential equations, but require an introduction to finite element methods will find this text crucial. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering which makes this book important for engineering students. This book focuses greatly on problem solving along with the mathematical aspects of the finite element method. This book is interesting and well written and is recommended for engineers or scientists who hold the practical aspect and want to dive deeper.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Mathematical Theory of Finite Elements – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter