Non-Funded Research Activity
Boundary Feedback Stabilisation Using Non-Conforming Finite Elements
Project leader:
- Prof. Dr. Peter Benner
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg, Germany
Tel: +49 (0)391-6110-450
E-mail: benner@mpi-magdeburg.mpg.de
-
Prof. Dr. Friedhelm Schieweck
Otto-von-Guericke-Universiät Magdeburg,
Institute for Analysis and Numerics,
Postfach 4120, 39106 Magdeburg, Germany
Tel: +49 (0)391-6720135
E-mail: schiewec@ovgu.de
- Dr. Jens Saak
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg, Germany
Tel: +49 (0)391-6110-216
E-mail: saak@mpi-magdeburg.mpg.de
- Dr. Piotr Skrzypacz
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg, Germany
Tel: +49 (0)391-67-18211
E-mail: skrzypacz@mpi-magdeburg.mpg.de
- Heiko Weichelt
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg, Germany
Tel: +49 (0)391-6110-414
E-mail: weichelt@mpi-magdeburg.mpg.de
- Project description:
-
We are investigating a new finite element method to improve boundary feedback stabilization
techniques of instationary, incompressible flow problems. Since standard finite elements do not
fulfill divergence freeness condition by themselves we cannot guarantee the validity of this condition after solving
the arising linear systems by iterative solvers. We, now, formulate the boundary feedback approach in operator terms
and solve the underlying PDE in each step, where the divergence freeness condition is handled inside the solver.
By using special finite elements we can improve the solver and end up with a fast robust algorithm.
- Related publications:
- @article{BenSSetal14,
author = {P. Benner and J. Saak and F. Schieweck and P. Skrzypacz and H.~K. Weichelt },
title = {A Non-Conforming Composite Quadrilateral Finite Element Pair for Feedback Stabilization of the {S}tokes Equations },
number = 3,
month = oct,
year = 2014,
journal = {Journal of Numerical Mathematics},
volume = 22,
pages = {191--220},
}
A Non-Conforming Composite Quadrilateral Finite Element Pair for Feedback Stabilization of the Stokes Equations;
Benner, Peter; Saak, Jens; Schieweck, Friedhelm; Skrzypacz, Piotr; Weichelt, Heiko K.;
Journal of Numerical Mathematics : Vol. 22, No. 3, pages 191-220;
deGruyter; 2014. ISBN/ISSN: 1570-2820
Earlier version as MPI-Preprint: MPIMD12-19. - Posters:
Non-Conforming Finite Elements and Riccati-Based Feedback Stabilization of the Stokes Equations, Jens Saak; 25th Chemnitz FEM Symposium 2012, 24-26 September, 2012.