Abstract
In this paper, we investigate the local ultraconvergence of k-degree (k≥3) finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes Th on a bounded rectangular domain D. The k-degree finite element estimates are developed for the Green's function and its derivatives. They are employed to explore the relationship among dist(x,∂D), dist(x,M) and the ultraconvergence of k-degree finite element methods at vertex x, where M is the set of corners of D. Numerical examples are conducted to demonstrate our theoretical results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
