Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Edition 3

This is an excellent introductory book to the theory of finite element methods. As any well-written textbook, it inevitably reflects some of the biases of the author's research which focuses on time-independent (mostly elliptic and saddle-point) problems. One main feature of the book is that it covers a wide spectrum of subjects: interpolation theory, Sobolev spaces, saddle-point problems and inf-sup conditions, multigrid and iterative solvers, as well as more ad-hoc subjects such as a posteriori error estimation, adaptive methods and non-conforming methods. The book does not go into too many details but it refers to more specialized publications. Many interesting examples and challenging exercises are provided. As with many books translated from German originals, the reading-flow gets stuck in some long sentences which may require from the inexperienced reader some patience to comprehend.