Finite Element Methods
Spring 2005


Prof. Dr. Ronald H.W. Hoppe


Contents:

Finite Element Methods are widely used discretization techniques for the numerical solution of PDEs based on appropriate variational formulations. We begin with basic principles for the construction of Conforming Finite Elements and Finite Element Spaces with respect to triangulations of the computational domain. Then, we study in detail a priori estimates for the global discretization error in various norms of the underlying function space. Nonconforming and Mixed Finite Element Methods will be addressed as well. A further important issue is adaptive grid refinement on the basis of efficient and reliable a posteriori error estimators for the global discretization error.


Prerequisites:

Calculus, Linear Algebra, Numerical Analysis


Textbooks:

D.Braess; Finite Elements. Theory, Fast Solvers and Application in Solid Mechanics. 2nd Edition. Cambridge Univ. Press, Cambridge, 2001
S.C. Brenner and L.Ridgway Scott; The Mathematical Theory of Finite Element Methods. 2nd Edition. Springer, New York, 2002
P.G. Ciarlet;The Finite Element Method for Elliptic Problems. Reprint. SIAM, Philadelphia, 2002



Time table:
Tuesday 1:00 - 2:30 pm Room 315 PGH
Thursday 1:00 - 2:30 pm Room 315 PGH



Script:
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8


Contact:

Prof. Dr. Ronald H.W. Hoppe Dipl.-Math. Christopher Linsenmann
Office: 669 PGH
Phone: (713) 743-3452
Fax: (713) 743-3505
Email: rohop@math.uh.edu
Office: 605 PGH
Phone:
Fax: (713) 743-3505
Email: linsen@math.uh.edu