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.8.10 The reference a#39; triangle and its symmetric b Q), :I LIL1 O L(2)(.Q) satisfies the inf-sup condition (8.2.16) for any k 2 2 if and only if each triangulation contains at least three triangles. Proof (Step I: necessary part). Let us show first that theanbsp;...
|Title||:||Mixed Finite Element Methods and Applications|
|Author||:||Daniele Boffi, Franco Brezzi, Michel Fortin|
|Publisher||:||Springer Science & Business Media - 2013-07-02|