A mixed finite element method for the stokes equations based on a weakly over-penalized symmetric interior penalty approach
Document Type
Article
Publication Date
2-1-2014
Abstract
We present a mixed finite element method for the steady-state Stokes equations where the discrete bilinear form for the velocity is obtained by a weakly over-penalized symmetric interior penalty approach. We show that this mixed finite element method is inf-sup stable and has optimal convergence rates in both the energy norm and the L 2 norm on meshes that can contain hanging nodes. We present numerical experiments illustrating these results, explore a very simple adaptive algorithm that uses meshes with hanging nodes, and introduce a simple but scalable parallel solver for the method. © 2013 Springer Science+Business Media New York.
Publication Source (Journal or Book title)
Journal of Scientific Computing
First Page
290
Last Page
307
Recommended Citation
Barker, A., & Brenner, S. (2014). A mixed finite element method for the stokes equations based on a weakly over-penalized symmetric interior penalty approach. Journal of Scientific Computing, 58 (2), 290-307. https://doi.org/10.1007/s10915-013-9733-9
