An optimal nonconforming finite element method for the Stokes equations
Jian Li
TL;DR
This paper introduces an improved, stable nonconforming finite element method for the Stokes equations using Crouzix-Raviart and linear elements, achieving optimal accuracy and robustness.
Contribution
It develops a new stabilized nonconforming finite element method for the Stokes equations with proven stability and optimal error estimates.
Findings
Method is stable and accurate
Achieves optimal order error estimates
Numerical results confirm robustness
Abstract
In this paper, we propose and develop an optimal nonconforming finite element method for the Stokes equations approximated by the Crouzix-Raviart element for velocity and the continuous linear element for pressure. Previous result in using the stabilization method for this finite element pair is improved and then proven to be stable. Then, optimal order error estimate is obtained and numerical results show the accuracy and robustness of the method.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods · Computational Fluid Dynamics and Aerodynamics