Abstract
This work proposes two nonconforming polynomial finite elements over general convex quadrilaterals. The first one is designed for fourth order elliptic singular perturbation problems, and the other works for Brinkman problems, approximating the velocity with piecewise constant pressure. We show the robustness of these methods, namely, the discrete solution converges uniformly in the given parameters of the corresponding model problem. Numerical examples are also provided.
2010 Mathematics Subject Classification:
Acknowledgements
The authors would also like to thank the editors and the anonymous reviewers for their helpful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.