Finite Element Methods and Domain Decomposition

The course considers the theory for finite element method to discrete partial differential equations, especially elliptical, and also solution techniques for the discrete equation system that become result. Domain decomposition as solving technique will become subject to special attention.

After completing the course, students will be able to:

• Formulate typical boundary value problems for elliptic equations in variational form that satisfies the conditions of the Lax-Milgram theorem.
• Discretize boundary value problems using the Galerkin approximation with the classic finite element methods.
• Develop simple programs in MATLAB to form systems of linear equations that approximates elliptic equations with finite element methods.
• Apply the theory of Hilbert spaces and polynomial approximation to prove the convergence of the finite element method.
• Use the multigrid method domain decomposition techniques for solving large systems of linear equations.

Autumn.