# Fast hp-FEM-solvers for the Stokes problem

## Dipl.-Math. Martin Purrucker

**April 27, 2010, 1:30 p.m. HS 13**

In this talk we investigate the construction of fast solvers for the solution of the discrete Stokes problem discretized by means of the hp-version of the finite element method (FEM) on a regular mesh with quadrilaterals. In order to guarantee the unique solvability of the arising indefinite linear system the spaces for the velocity and the pressure variables have to be chosen in such a way that a discrete inf-sup-condition holds. Furthermore the size of this inf-sup-constant has also major influence on the approximation properties as well as the construction of a preconditioner for the pressure Schur complement of the arising system. In this talk we discuss several common choices of pairs of spaces for velocity and pressure and investigate the behaviour of the inf-sup-constant.