P- and hp- finite element methods : theory and applications in solid and fluid mechanics
著者
書誌事項
P- and hp- finite element methods : theory and applications in solid and fluid mechanics
（Numerical mathematics and scientific computation）
Clarendon Press, 1998
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注記
Includes bibliographical references and Index
内容説明・目次
内容説明
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.
目次
- Variational formulation of boundary value problems
- The Finite Element Method (FEM): definition, basic properties
- hp- Finite Elements in one dimension
- hp- Finite Elements in two dimensions
- Finite Element analysis of saddle point problems, mixed hp-FEM in incompressible fluid flow
- hp-FEM in the theory of elasticity
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