Numerical solution of Variational Inequalities by Adaptive Finite Elements

Franz-Theo Suttmeier (Autor)

Buch | Softcover

X, 161 Seiten

2008
Vieweg & Teubner (Verlag)
978-3-8348-0664-2 (ISBN)

Infos

This work describes a general approach to a posteriori error estimation and adaptive mesh design for ?nite element models where the solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a posteriori error estimates with respect to arbitrary functionals of the error. In these estimates local residuals of the computed solution are multiplied by sensitivity factors which are obtained from a - merically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored - cording to the particular goal of the computation. This method is developed here for several model problems. Based on these examples, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities. F¨ ur Alexandra, Katharina und Merle Contents 1 Introduction 1 2 Models in elasto-plasticity 13 2. 1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . 14 2. 2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 The dual-weighted-residual method 23 3. 1 A model situation in plasticity . . . . . . . . . . . . . . . . . . 24 3. 2 A posteriori error estimate . . . . . . . . . . . . . . . . . . . . . 25 3. 3 Evaluation of a posteriori error bounds . . . . . . . . . . . . . . 26 3. 4 Strategies for mesh adaptation . . . . . . . . . . . . . . . . . . 28 3. 5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 Extensions to stabilised schemes 33 4. 1 Discretisation for themembrane-problem . . . . . . . . . . . . 35 4. 2 A posteriori error analysis . . . . . . . . . . . . . . . . . . . . . 37 4. 3 Numerical tests . . . . . . . . . . . . . . . . . . . . . . . . . . .

Autor

Dr. Franz-Theo Suttmeier is a professor of Scientific Computing at the Institute of Applied Analysis and Numerics at the University of Siegen.

Inhalt

Models in elasto-plasticity.- The dual-weighted-residual method.- Extensions to stabilised schemes.- Obstacle problem.- Signorini's problem.- Strang's problem.- General concept.- Lagrangian formalism.- Obstacle problem revisited.- Variational inequalities of second kind.- Time-dependent problems.- Applications.- Iterative Algorithms.- Conclusion.

Produkt-Details

• Erscheint lt. Verlag: 28.8.2008
• Reihe/Serie: Advances in Numerical Mathematics
• Zusatzinfo: X, 161 p.
• Verlagsort: Wiesbaden
• Sprache: englisch
• Maße: 148 x 210 mm
• Gewicht: 260 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: Adaptivität • A Posteriori Fehlerschätzung • A Priori Fehlerschätzung • Equation • Finite • Finite-Elemente-Methode • Finite-Elemente-Methode (FEM) • Finite Element Method • Mathematics • Ungleichungen • Variationsungleichungen
• ISBN-10: 3-8348-0664-1 / 3834806641
• ISBN-13: 978-3-8348-0664-2 / 9783834806642
• Zustand: Neuware