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Error-controlled Adaptive Finite Elements in Solid Mechanics




Error-controlled Adaptive Finite Elements in Solid Mechanics


Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic.
This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications.
* First book to go beyond the Finite Element Method in itself
* Covers material from a new research area
* Presents benchmarks of 2D- and 3D- applications
* Fits with the new trend for genetic strategies in engineering

Introduction (Stein).

Error Estimation and Adaptive Mesh Design for FE Models in Elasto-Plasticity Theory (Rannacher and Suttmeier).

Adaptive FEM for elasto-plastic Deformations (Stein and Schmidt).

Numerical Simulation of Localization Phenomena in Geomechanics by Entended Continuum Formulations (Wunderlich et al).

Adaptive Methods for Contact Problems (Rieger et al).

An Adaptive Boundary Element Method for Contact Problems (Eck et al).

Goal-Oriented Error Estimation in Solid Mechanics (Steeb,Maute and Ramm).

The p-version of the Finite Element Method for Structural Problems (Rank et al).

Adaptive Analysis of Plate and Shell Structures Under Transient Loading (Schweizerhof, Neumann and Riccius).

The Application of Adaptive Parallel Multigrid Methods to Problems in Nonlinear Solid Mechanics (Lang, Wieners and Wittum).

Benchmarks (Stein et al).