Abstract
This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works, we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e., the first order accuracy of the velocities in H 1-norm and the pressure in L 2-norm, as well as the second order accuracy of the velocities in L 2-norm. Besides, we clarify the differences between rectangular and quadrilateral finite element approximation. In addition, we give several examples to verify the validity of our error estimates.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.