Minerva Logo of the MPG

Computational Methods in Systems and Control Theory


Non-Funded Research Activity

Boundary Feedback Stabilisation Using Non-Conforming Finite Elements




Project leader: Researcher: Duration: since February 2012

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.





©2018, Max Planck Society, Munich
Heiko Weichelt, weichelt@mpi-magdeburg.mpg.de
11 Januar 2016