Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 26–July 1, 2006

  • Daniele Boffi
  • Franco Brezzi
  • Leszek F. Demkowicz
  • Ricardo G. Durán
  • Richard S. Falk
  • Michel Fortin
  • Daniele Boffi
  • Lucia Gastaldi

Part of the Lecture Notes in Mathematics book series (LNM, volume 1939)

Table of contents

  1. Front Matter
    Pages i-x
  2. Ricardo G. Durán
    Pages 1-44
  3. Daniele Boffi, Franco Brezzi, Michel Fortin
    Pages 45-100
  4. Richard S. Falk
    Pages 159-194
  5. Richard S. Falk
    Pages 195-232
  6. Back Matter
    Pages 233-235

About this book


Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems.

This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.


Maxwell's equations approximation of partial differential equations computational elasticity computational electromagnetism computational fluid-dynamics finite element method mixed finite elements

Authors and affiliations

  • Daniele Boffi
    • 1
  • Franco Brezzi
    • 2
  • Leszek F. Demkowicz
    • 3
  • Ricardo G. Durán
    • 4
  • Richard S. Falk
    • 5
  • Michel Fortin
    • 6
  1. 1.Dipartimento di MatematicaUniversità degli Studi di BresciaItaly
  2. 2.Istituto Universitario di Studi SuperioriIstituto di Matematica Applicata e Tecnologie Informatiche del C.N.R27100Italy
  3. 3.Institute for Computational Engineering and SciencesThe University of Texas at Austin78712AustinUSA
  4. 4.Departamento de MatemáticaUniversidad de Buenos Aires1428Argentina
  5. 5.Department of MathematicsThe State University of New Jersey08854-801PiscatawayUSA
  6. 6.Département de mathématiques et de statistiquePavillon Alexandre-Vachon Université LavalQuébecCanada

Editors and affiliations

  • Daniele Boffi
    • Lucia Gastaldi
      • 1
    1. 1.Dipartimento di MatematicaUniversità degli Studi di BresciaItaly

    Bibliographic information

    • DOI
    • Copyright Information Springer Berlin Heidelberg 2008
    • Publisher Name Springer, Berlin, Heidelberg
    • eBook Packages Mathematics and Statistics
    • Print ISBN 978-3-540-78314-5
    • Online ISBN 978-3-540-78319-0
    • Series Print ISSN 0075-8434
    • Buy this book on publisher's site
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