Finite Element Methods are used in numerous engineering applications where numerical solutions of partial differential equations are needed. This book deals with the Finite Element Method, while also covering areas such as automatic adaptation and error estimation, and aspects of the method's adaptivity.

This book contains the numerical methods, mathematical analysis, algorithms, software aspects and comparative results of a six year joint project of nine German University institutes, supported by the German National Science Foundation (DFG).

It covers new progress for efficient and reliable error estimates mainly of the Finite Element Method for non-linear problems in solid mechanics, as well as efficient re-meshing techniques and solution algorithms.

Topics covered include:
* Elastoplastic deformations and contact problems

* Shear localization of inelastic deformations

* Thin-walled structures

* Elastodynamics
The authors, all experts in computational mechanics, provide a wealth of new ideas for the next generation of software for adaptive finite elements, which will be of great interest to industry. Each chapter includes the state of the art, comparisons between different methods and the mechanical and mathematical background of the methods addressed. Practising engineers, researchers and students in engineering, applied mathematicians and computer scientists will find new material for developing, maintaining and applying finite element algorithms which reach new heights of approximation quality.