Finite Elements

(this page is still under construction)

In many applications in computational science and engineering partial differential equations have to be solved. As often an analytical solution is not readily available, approximate solutions are sought for. Besides finite difference methods and finite volume methods, finite element methods are often used in practice. From a mathematical viewpoint finite element methods are the natural discrete approximation of weak solutions in Sobolev spaces, as they are known from functional analysis. From a practical perspective, they are a versatile tool for the unstructured discretization of PDEs.
The course covers the following topics:

• Sobolev spaces and background from functional analysis
• Conforming finite elements
• Non-conforming finite elements
• Mixed finite elements
• Error estimates
• Consideration of the implementation

A background in functional analysis and numerical methods for PDEs is helpful but not required.