Higher-Order Finite Element Methods
1st Edition
Published on 28. July 2003
Book
Hardback
404 pages
978-1-58488-438-5 (ISBN)
Description
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales.
Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity.
Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.
Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity.
Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.
Reviews / Votes
"[A] large number of constructions on hp finite elements ... are collected and presented in a unified and consistent way. In this respect the book is timely, very useful, and quite unique. ... [The book] contains many detailed constructions, interesting concepts, and practical discussions. ... It could be used as a reference book and/or a supplement to a course on discretization methods for differential equations."- Mathematics of Computation, April 2005
"This book is a valuable addition to the existing literature on adaptive hp-finite element methods [1, 2, 3] and provides the practitioner with the necessary tools and techniques for understanding and implementing high-order hierarchic finite element methods. ... Overall this is a useful and well-written text. ... I recommend the book for applied mathematicians and practitioners using the finite element method."
- SIAM Review
"This book gives a very thorough explanation of how to construct an hp-finite-element computer program."
-Zentralblatt MATH
"... a timely and balanced introduction to the very active research area of hp-adaptive methods for the solution of partial differential equations. ... The detailed overview of element types and quadrature rules provides a valuable reference, while the discussion of suitable data structures and efficient linear solvers provide an excellent introduction to key aspects, often neglected, of this class of methods. ... a delightful introduction to these rapidly expanding research areas."
- Jan S. Hesthaven, Division of Applied Mathematics, Brown University
"... the overall structure of this comprehensive monograph is very transparent and the style of presentation of the material has an expository nature. ... There is no doubt that this new monograph on recent topics of finite element theory and applications will be welcomed by the broad community of finite element researchers and lecturers, both by the practitioners and by the numerical functional analysts."
- Roger Van Keer, Ghent University, Belgium
"....Summing up, the book is well-written, and the overall structure is clear and well-explained. I think that it surely will meet the interest of applied mathematician, engineers, and practitioners."
-Alberto Valli, Universita Degli Studi Di Trento, Italy
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
Professional and scholarly
College/higher education
Professional
Illustrations
202 s/w Abbildungen, 78 s/w Tabellen
78 Tables, black and white; 202 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
725 gr
ISBN-13
978-1-58488-438-5 (9781584884385)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Pavel Solin | Karel Segeth | Ivo Dolezel
Higher-Order Finite Element Methods
E-Book
07/2003
1st Edition
Chapman and Hall
€264.99
Available for download
Pavel Solin | Karel Segeth | Ivo Dolezel
Higher-Order Finite Element Methods
E-Book
07/2003
1st Edition
Chapman and Hall
€264.99
Available for download
Persons
Pavel Solin, Karel Segeth, Ivo Dolezel
Content
Introduction. Hierarchic Master Elements of Arbitrary Order. Higher-Order Finite Element Discretization. Higher-Order Numerical Quadrature. Numerical Solution of Finite Element Equations. Mesh Optimization, Reference Solutions, and hp-Adaptivity.