p- and hp- Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics

Hardcover | August 1, 1998

byC. SchwabAs told byCh Schwab

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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 typicallyarise 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 pointproblems 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.

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From the Publisher

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 emerge...

C. Schwab is at the Seminar fur Angewandte Mathematik, ETH, Zurich.

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Format:HardcoverPublished:August 1, 1998Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198503903

ISBN - 13:9780198503903

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Table of Contents

Variational formulation of boundary value problemsThe Finite Element Method (FEM): definition, basic propertieshp- Finite Elements in one dimensionhp- Finite Elements in two dimensionsFinite Element analysis of saddle point problems, mixed hp-FEM in incompressible fluid flowhp-FEM in the theory of elasticity

Editorial Reviews

'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 highlyrecommended to anybody with mathematical interest for both learning and reference' ZAMM