Mixed Finite Element Methods and Applications

✍ Scribed by Daniele Boffi, Franco Brezzi, Michel Fortin (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 691
• Series: Springer Series in Computational Mathematics 44
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiv
Variational Formulations and Finite Element Methods....Pages 1-46
Function Spaces and Finite Element Approximations....Pages 47-121
Algebraic Aspects of Saddle Point Problems....Pages 123-195
Saddle Point Problems in Hilbert Spaces....Pages 197-263
Approximation of Saddle Point Problems....Pages 265-335
Complements: Stabilisation Methods, Eigenvalue Problems....Pages 337-399
Mixed Methods for Elliptic Problems....Pages 401-457
Incompressible Materials and Flow Problems....Pages 459-538
Complements on Elasticity Problems....Pages 539-573
Complements on Plate Problems....Pages 575-623
Mixed Finite Elements for Electromagnetic Problems....Pages 625-662
Back Matter....Pages 663-685

✦ Subjects

Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Theoretical and Applied Mechanics