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Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
List of contents
Preface.- Variational Formulations and Finite Element Methods.- Function Spaces and Finite Element Approximations.- Algebraic Aspects of Saddle Point Problems.- Saddle Point Problems in Hilbert spaces.- Approximation of Saddle Point Problems.- Complements: Stabilisation Methods, Eigenvalue Problems.- Mixed Methods for Elliptic Problems.- Incompressible Materials and Flow Problems.- Complements on Elasticity Problems.- Complements on Plate Problems.- Mixed Finite Elements for Electromagnetic Problems.- Index.
About the author
Franco Brezzi is Editor-in-Chief of the journal Numerische Mathematik and co-author of several Springer books, among others the classical book SSCM Vol. 15 "Mixed and Hybrid Finite Element Methods" with Michel Fortin.
Summary
Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
Additional text
From the book reviews:
“It is very useful for mathematicians as well as practitioners of finite element methods. The book is divided into 11 chapters.” (Beny Neta, Mathematical Reviews, April, 2014)
“The new book is an extended and corrected revision after 20 years, which is based on the previous material. … one obtains a quite complete overview on the development of nearly all relevant techniques for the construction of a stable mixed method. This makes this monograph a valuable reference for researchers in the field which may replace the first edition on the bookshelf.” (Christian Wieners, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 94 (9), 2014)
Report
From the book reviews:
"It is very useful for mathematicians as well as practitioners of finite element methods. The book is divided into 11 chapters." (Beny Neta, Mathematical Reviews, April, 2014)
"The new book is an extended and corrected revision after 20 years, which is based on the previous material. ... one obtains a quite complete overview on the development of nearly all relevant techniques for the construction of a stable mixed method. This makes this monograph a valuable reference for researchers in the field which may replace the first edition on the bookshelf." (Christian Wieners, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 94 (9), 2014)
