Adaptive Finite Element Methods for Differential Equations

Bangerth, Wolfgang; Rannacher, Rolf

ISBN 10: 3764370092 / ISBN 13: 9783764370091

Editore: Birkhauser Verlag AG, 2003

Riguardo questo articolo

Series: Lectures in Mathematics. ETH Zurich. Num Pages: 216 pages, 151 black & white illustrations, biography. BIC Classification: PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 244 x 170 x 11. Weight in Grams: 416. . 2003. Softcover reprint of the original 1st ed. 2003. Paperback. . . . . Books ship from the US and Ireland.

Codice articolo V9783764370091

Dati bibliografici

• Titolo: Adaptive Finite Element Methods for Differential Equations
• Editore: Birkhauser Verlag AG
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 3764370092
• ISBN 13: 9783764370091
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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.