P- And HP- Finite Element Methods : Theory and Applications to Solid and Fluid Mechanics

Christoph Schwab

ISBN 10: 0198503903 / ISBN 13: 9780198503903

Editore: Oxford University Press (UK) Jan 1999, 1999

Riguardo questo articolo

Neuware - This book is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics. In the last decade the p-, hp-, and spectral element methods have emerged as efficient and robust approximation methods for several classes ofproblems in this area. The aim of this book is to establish the exponential convergence of such methods for problems with the piecewise analytic solutions which typically arise in engineering. It looks at the variational formulation of boundary value problems with particular emphasis on theregularity of the solution. The books then studies the p- and hp- convergence of the finite element method (FEM) in one and two dimensions, supplying complete proofs. Also covered are hp-FEM for saddle point problems and the techniques for establishing the discrete infsup condition. Finally, hp-FEMin solid mechanics and the issue of locking is addressed in the context of these methods. It is suitable for graduate students and researchers who have had some prior exposure to FEM.

Codice articolo 9780198503903

Dati bibliografici

• Titolo: P- And HP- Finite Element Methods : Theory and Applications to Solid and Fluid Mechanics
• Editore: Oxford University Press (UK) Jan 1999
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 0198503903
• ISBN 13: 9780198503903
• Rilegatura: Buch
• Condizione: Neu

Descrizione articolo

Riassunto

This book is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics, and is suitable for graduate students and researchers who have had some prior exposure to finite element methods (FEM). In the last decade the p-, hp-, and spectral element methods have emerged as efficient and robust approximation methods for several classes of problems in this area. The aim of this book is therefore to establish the exponential convergence of such methods for problems with the piecewise analytic solutions which typically arise in engineering. It looks at the variational formulation of boundary value problems with particular emphasis on the regularity of the solution. The books then studies the p- and hp- convergence of FEM in one and two dimensions, supplying complete proofs. Also covered are hp-FEM for saddle point problems and the techniques for establishing the discrete infsup condition. Finally, hp-FEM in solid mechanics and the issue of locking is addressed in the context of these methods.

Recensione

'Summarizing the book is the first theoretical book addressing the hp-version of the finite element method which is used today in practical computations. It is very well written and gives a very good review of the techniques and results in this relatively new direction in the FEM. It is highly recommended to anybody with mathematical interest for both learning and reference' ZAMM