Applied Finite Elements

Finite element methods provide accurate and efficient numerical techniques to solve partial differential equations. These equations model a wide variety of physical and technical problems and can generally only be solved with numerical techniques. Finite elements offer a great flexibility to deal with complex domains, adaptivity and are supported with a highly developed mathematical theory.

This course aims at teaching the basic concepts of finite element methods, with emphasis on partial differential equations (pde’s). The focus is on practical aspects, how to construct and solve finite element discretizations for a variety of pde’s and apply these techniques to realistic model problems by making your own finite element programs. This course focuses on the practical aspects of FEM, the theoretical foundation is discussed in the course Mathematical Theory of Finite Element Methods, code 15509.
 

The following topics will receive attention:

1. Introduction and a crash course on pde’s.
2.  Minimization problems and their numerical solution with finite element methods.
3. Weak formulation of partial differential equations and Galerkin’s method, with application to elliptic pde’s and the convection-diffusion equation.
4. Extension of FEM, quadratic triangles, quadrilaterals, curved boundaries, strongly elliptic systems and the Stokes equation.
5.  Overview of solution techniques for large systems of equations.
6. Time dependent problems, method of lines.
7. Solving realistic model problems by writing sample finite element programs

J.J.W. van der Vegt (UT) j.j.w.vandervegt@math.utwente.nl
F.J. Vermolen (TUD), f.vermolen@tudelft.nl
J.M.L. Maubach (TUE), j.m.l.maubach@tue.nl
O. Bokhove (local support exercises for UT) o.bokhove@ewi.utwente

This course is an intensive course and therefore only master students can participate.