Error-Controlled Adaptive Finite Elements in Solid Mechanics
Chapter One
Introduction
Erwin Stein
1.1 ERROR-CONTROLLED ADAPTIVE FINITE-ELEMENT-METHODS
The important advantages of direct variational methods, in particular the Finite Element
Method (FEM), against Finite Difference Methods (FDM) are what we call 'logical width
and depth, combined with simplicity and robustness', i.e. the same additive methodological
concept for a wide class of problems with simple extension to more complicated problems
(e.g. from linear to nonlinear theories), and this should be possible with simple algorithmic
structures like symmetric and positive definite systems matrices combined with
robustness of the solvers and parameter-independent convergence rates in regular cases.
The accuracy of a specific FE analysis thus depends upon the mathematical model and
its dimension, the given physical problem, the polynomial degree pread full excerpt from Error-controlled Adaptive Finite Elements in Solid Mechanics ebook
