Adaptive Finite Element Methods for Differential Equations

These 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 it 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 practical exercises, sample programs are provided via internet.

Additional text

"Most graduate students in engineering and physical sciences should be able to handle the material without excessive difficulty. The presentation is very much a tutorial approach promoting a hands-on experience, reinforced with practical exercises at the end of each chapter, aimed towards practitioners.... [The] present book provides a gentler introduction for the beginning graduate student or nonspecialist practitioner."
— SIAM Review 
 

Product details

• Authors: Wolfgang Bangerth, Rolf Rannacher
• Publisher: Springer Nature EN
• Languages: English
• Product format: Paperback / Softback
• Released: 23.01.2003
• EAN: 9783764370091
• ISBN: 978-3-7643-7009-1
• No. of pages: 208
• Dimensions: 170 mm x 244 mm x 19 mm
• Weight: 420 g
• Illustrations: VIII, 208 p. 151 illus., schwarz-weiss Illustrationen
• Series: Lectures in Mathematics. ETH Zürich
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Klassische Mechanik, Mathematics and Statistics, Classical mechanics, Classical and Continuum Physics, Computational Mathematics and Numerical Analysis, Ordinary Differential Equations, Continuum physics, Computer mathematics, Numerical analysis, Differential equations