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 (auth.), Daniele Boffi, Lucia Gastaldi (eds.)9783540783145, 3540783148, 3540783199

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.

Table of contents :
Front Matter….Pages i-x
Mixed Finite Element Methods….Pages 1-44
Finite Elements for the Stokes Problem….Pages 45-100
Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations….Pages 101-158
Finite Element Methods for Linear Elasticity….Pages 159-194
Finite Elements for the Reissner–Mindlin Plate….Pages 195-232
Back Matter….Pages 233-235