## Adaptive finite element methods for differential equations

### Wolfgang Bangerth, Rolf Rannacher

From the back cover of the book:
The present lecture notes discuss concepts of "self-adaptivity" in the
numerical solution of differential equations, with emphasis on
Galerkin finite element methods. The key issues are a posteriori error
estimation and automatic mesh adaptation. Besides the traditional
approach of energy-norm error control, a new duality-based technique,
the Dual Weighted Residual method for goal-oriented error estimation,
is discussed in detail. This method aims at economical computation of
arbitrary quantities of physical interest by properly adapting the
computational mesh. This is typically required in the design cycles of
technical applications. For example, the drag coefficient of a body
immersed in a viscous flow is computed, then it is minimized by
varying certain control parameters, and finally the stability of the
resulting flow is investigated by solving an eigenvalue
problem. "Goal-oriented" adaptivity is designed to achieve these tasks
with minimal cost.

At the end of each chapter some exercises are posed in order to assist
the interested reader in better understanding the concepts
presented. Solutions and accompanying remarks are given in the
Appendix. For the pratical exercises, sample programs are provided via
internet.

*Wolfgang Bangerth*

*2004-01-22*