Numerical Solution of Partial Differential Equations by the Finite Element Method Paperback – Jan 15 2009
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1. A strong background in mathematical analysis is required to understand the proofs.
2. Few implementation details provided.
3. Focus is primarily on elliptic PDEs. Only 1 chapter each for Parabolic and Hyperbolic PDEs.
This was the textbook I had for a grad math course in FEM. I had previously studied FEM on my own through an engineering text. Engineering FEM books explain FEM through a bottom-up approach: formulating the elements and then assembling them. Mathematical FEM books explain FEM through a top-down approach: formulating the solution space and then specifying the elements. This book follows the mathematical approach, so you will not find it useful in terms of implementation or applications. However, the proofs are fairly easy to follow (for a mathematician).
- as already observed by another reviewer, it is typed in something like Word instead of Latex, hence reading lots of equations is a painful experience !
- it is light on discontinuous Galerkin method and heavy on the streamline diffusion method since the latter was the most promising method at the time this little book was written; since then, the streamline diffusion method is dead and the discontinuous Galerkin method is the standard FE extension to deal with hyperbolic system of equations.
If it does not suffice:
- no Matlab / Octave source code to illustrate
- no errata
- no solution to the exercises
either in the book or on the author's home page.
Nevertheless, at this very low price, I would recommend it for a concise introduction.
Among the many books devoted to the subject, that by C. Johnson is definitely one of the best; my opinion is that no other book can introduce you to the method as seamlessly, yet accurately, as this book does. I strongly suggest the book to anyone interested in the subject. Despite its age (first published in 1987), it is still extremely useful.
I would recommend this book to engineers who are starting to use FEM analysis, and graduate students who are learning the basics of FEM.