Robust nonconforming polynomial finite elements over quadrilaterals

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.

Keywords:

• Nonconforming finite element
• polynomial
• convex quadrilateral
• singular perturbation
• uniform convergence

2010 Mathematics Subject Classification:

• 65N30

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.

Additional information

Funding

This project is supported by National Natural Science Foundation of China (NNSFC) [grant numbers 61733002, 61720106005, 61702244, 61772105] and ‘the Fundamental Research Funds for the Central Universities’.