I will introduce and discuss several iterative methods such as fixed-point iteration, Anderson acceleration method, Uzawa algorithm, and generalized minimum residual method (GMRES). These numerical schemes are utilized to approximate the solution to a symmetric, indefinite linear algebra system called a saddle point system. The system often arises in computational fluid dynamics and can be derived from fluid flow equations by a finite element method. I will use a couple of test cases to illustrate the convergence of different iterative methods applied to the system.

The talk will be accessible for students. Students who are interested in learning about scientific computing/numerical linear algebra are encouraged to come.