Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776557 | Applied Numerical Mathematics | 2017 | 28 Pages |
Abstract
We present an analysis of a set of parametrized boundary conditions for a Stokes-Brinkman model in two space dimensions, discretized by finite elements. We particularly point out an instability which arises when these boundary conditions are posed on a curved line, which then leads to unphysical oscillations. In contrast to a Navier-slip condition, which is prone to Babuška's paradox, this instability can be traced back to the continuous level. We claim that the stability in these cases depend on the amount of curvature at the boundary, which is shown in a reduced setting in cylinder coordinates. The transition to a two dimensional Cartesian case is then based on numerical studies, which further substantiate the claim. Lastly, stabilization techniques are motivated that enhance the continuous FEM setting and are conveniently able to deal with arising oscillations.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Armin Westerkamp, Manuel Torrilhon,