Abstract
We consider the widely used continuous $Q_{k+1}-Q_k$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schoberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems, including some numerical studies of the parallel performance of the matrix-free monolithic multigrid solvers proposed.
Brief Biography
Prof. Dr. Ulrich Langer is a Professor at the Institute of Numerical Mathematics, Johannes Kepler University Linz. He obtained his doctoral degree from the State University of St. Petersburg, Russia, and has a habilitation in mathematics from the Technical University of Chemnitz. His research interests encompass the numerical solution of partial differential equations, structure-preserving discretization, efficient solvers for linear systems, and nonlinear optimization.
