Rational Bases and Generalized Barycentrics Applications to Finite E
This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions f
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Rational Bases and Generalized Barycentrics Applications to Finite Elements and Graphics
Rational Bases and Generalized Barycentrics
Eugene Wachspress
Rational Bases and Generalized Barycentrics Applications to Finite Elements and Graphics
123
Eugene Wachspress Department of Civil Engineering and Engineering Mechanics Columbia University New York, NY, USA
Wachspress, E.: A Rational Finite Element Basis. New York, Academic Press. 1975.
ISBN 978-3-319-21613-3 DOI 10.1007/978-3-319-21614-0
ISBN 978-3-319-21614-0 (eBook)
Library of Congress Control Number: 2015945110 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
Dedication in my 1975 book on A Rational Finite Element Basis
To my parents, Jean and Sidney Wachspress
This work is dedicated to my grandchildren Yael, Akili, Sudi, Jacob, Anna and Benjamin who must confront the problems left by my generation.
Preface: Part I
Popularity of the finite element method is such that an astute lecturer or author may increase his audience by choice of a title like “Finite Elements and : : :,” inserting his topic in the blank space, no matter how remotely connected with finite element methods. The title of this book is, nevertheless, precisely the subject of this book. Fundamental to any finite element computation is the definition of an approximation space over a collection of elements. A basis function is associated with each element node so that the approximation within the element is determined by the nodal values. Polynomial basis functions have been widely used, and convergence theory for continuous patchwork polynomial approximation has been developed to a high degree of mathematical sophistication. Elements over which polynomial basis functions apply, within restrictions impos
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