Focusing on non-standard finite element methods, this text by Brezzi and Fortin offers a comprehensive framework for understanding their rapid evolution. It examines classic examples such as Dirichlet's problem, the Stokes problem, and linear elasticity. Through detailed analysis, the authors aim to elucidate the properties of these methods, providing insights that enhance the reader's grasp of the subject.
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.
Ausstellung im Antikenmuseum Basel und Sammlung Ludwig, 3. November 1999 bis 31. März 2000