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 of problems 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 the regularity 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-FEM in 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.
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C. Schwab is at the Seminar fur Angewandte Mathematik, ETH, Zurich.Review:
"This is a volume in the series Numerical Mathematics and Scientific Computation. Finite element methods (FEM) are discretizations of boundary value problems in variational form. In the h-version FEM convergence is achieved by mesh refinement; in the p-version, it is achieved by increasing polynomial degree. This book resulted from a graduate course on FEM taught at the ETH, Zurich, to mathematicians and engineers who were interested in learning the mathematical basis for the recent higher-order, hp and spectral element methods. The investigation of the relative merits of higher-order methods over the classical h-version approach requires a careful look at the regularity of solutions of elliptic boundary value problems. . . . There are appendices on Sobolev and interpolation spaces, and orthogonal polynomials. The bibliography contains 152 items."--Quarterly of Applied Mathematics
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Buchbeschreibung Oxford Univ Pr on Demand, 1999. Hardcover. Buchzustand: Fine. First Edition. Clean no highlights or remarks inside. 374 pages with the index. hardcover textbook binding.We ship from the USA and Canada. Artikel-Nr. 17446