Presents a survey of intrinsic techniques and practical implementation of higher-order finite element schemes. This book addresses automatic hp-adaptivity in one and two spatial dimensions. It includes a discussion of suitable data structures and efficient linear solvers. It is suitable for both applied mathematicians and engineers.
Higher-Order Finite Element Methods provides an exhaustive survey of intrinsic techniques and practical implementation of higher-order finite element schemes. It addresses automatic hp-adaptivity in one and two spatial dimensions and includes up-to-date references to ongoing research related to automatic hp-adaptivity in 3D. The authors' discussion of suitable data structures and efficient linear solvers provides an excellent introduction to key, often neglected aspects of this class of methods. Avoiding heavy mathematical jargon where possible, the book is clear, comprehensive, and designed for both applied mathematicians and engineers who are interested in finite elements.
"[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
