The Finite Element Method: Theory, Implementation, and Applications (Texts in Computational Science and Engineering, 10) 2013th Edition by Mats G. Larson (PDF)

Description

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

User’s Reviews

Editorial Reviews: Review From the reviews:“The authors give an introduction to the finite element method as a general computational method for solving partial differential equations (PDEs) approximately. … The book should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed.” (Răzvan Răducanu, Zentralblatt MATH, Vol. 1263, 2013) From the Back Cover This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a helpful review of finite element method use in MATLAB. You will definitely have to review the PDE toolbox on the Mathworks website, as the code here is mostly home brewed. This is a good starting point though. The best features of this book are the firm mathematical establishment of FEM – it would have been unnecessary and prohibitive to some readers to use more advanced mathematics and delve deeper into the analytical theory – and the thorough, if sometimes brief, coverage of almost all aspects of FEM. The combination of MATLAB code and an understandable basis in mathematical theory definitely made this book worth the read. The electromagnetics section is well presented (I haven’t yet read the transport, solid mechanics, and fluid mechanics sections). However, electrons are not magnetic monopoles!Unfortunately, I can’t give this work 5 stars because of the numerous typos. They sometimes make it a little difficult to understand what the authors are saying. It is obvious that the writers have a poor command of English. I was puzzled by the continual use of odd phrases with the words “ditto,” “origo,” “ansatz,” and etc. The editor definitely failed in his duty. The notation for the physical science embedded within the work is not great, but it can be understood without much effort. Despite these shortcomings, the book is still good.

⭐concepts are well explained and the material has a good flow. unfortunately the book is plagued with errors. throughout the text from codes, equations, results of codes, sentences all the way to grammar …sometimes it gets really frustrating to figure out what should be there and is not.Springer must take responsibility for publishing and selling a poorly edited book.it is not the first time I come across Springer product with so many typos. I would say is a waste of money until a newly edited edition comes out.

⭐The worst book I have ever bought since highschool. It is too superficial, unstructured. It is definitely clear that the authors do not know how to address the mathematical concepts to readers. I would definitely not recommend to buy this book ever.

⭐Natürlich würde ich nochmals kaufen! Vielen Dank…Ps: Es wäre vielleicht besser, wenn die Verfolgungsaktionen der Bestellung besser beschrieben worden wäre…

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