Courses › Course Material › Course Material

Synopsis for Mixed Finite Element Methods and Iterative Methods


Number of lectures: 12 TT

Course Description

Part I: Mathematical Theory of Mixed Finite Element Methods
  1. Examples of mixed variational formulations in continuum mechanics. [1 lecture]
  2. Abstract mixed formulation. [1 lecture]
  3. Discrete mixed formulation. [1 lecture]
  4. Convergence results. [1 lecture]
  5. The discrete inf-sup condition. [1 lecture]
  6. Veri fication of the discrete inf-sup condition. [1 lecture]
Part II: Iterative methods and preconditioning for Mixed Finite Elements
  1. Matrix structure and properties [1 lecture]
  2. Iterative methods [2 lectures]
  3. Preconditioning [2 lectures]
  4. Convergence [1 lecture]

Reading List

  1. S.C. Brenner and L.R. Scott (2008) The Mathematical Theory of Finite Element Methods, Third edition, Texts in Applied Mathematics, Vol. 15. Springer, New York.
  2. H.C. Elman, D.J. Silvester, and A.J. Wathen (2005) Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics, Numerical Mathematics and Scienti c Computation, Oxford University Press, New York.
For additional reading see
  1. F. Brezzi and M. Fortin (1991) Mixed and hybrid fi nite element methods, Springer Series in Computational Mathematics, Vol. 15, Springer-Verlag, New York.
  2. V. Girault and P.-A. Raviart (1986) Finite Element Methods for Navier-Stokes equations, Springer Series in Computational Mathematics, Vol. 5, Springer-Verlag, Berlin.

Last updated by Endre Suli on Tue, 14/05/2013 - 7:17pm.
This page is maintained by Kathryn Gillow. Please use the contact form for feedback and comments.