Superconvergence Analysis of Curlcurl-Conforming Elements on Rectangular Meshes
Document Type
Article
Publication Date
5-1-2023
Abstract
In our recent work (Hu et al. in SIAM J Sci Comput 42(6):A3859–A3877, 2020), we observed numerically some superconvergence phenomena of the curlcurl-conforming finite elements on rectangular domains. In this paper, we provide a theoretical justification for our numerical observation and establish a superconvergence theory for the curlcurl-conforming elements on rectangular meshes. For the elements with parameters r (r= k- 1 , k, k+ 1) and k (k≥ 2), we show that the first (second) component of the numerical solution uh converges with rate r+ 1 at r vertical (horizontal) Gaussian lines in each element when r= k- 1 , k with k≥ 3 , ∇ × uh converges with rate k+ 1 at k2 Lobatto points in each element when k≥ 3 , and the first (second) component of ∇ × ∇ × uh converges with rate k at (k- 1) horizontal (vertical) Gaussian lines when k≥ 2. They are all one-order higher than the related optimal rates. More numerical experiments are provided to confirm our theoretical results.
Publication Title
Journal of Scientific Computing
Recommended Citation
Wang, L.,
Zhang, Q.,
&
Zhang, Z.
(2023).
Superconvergence Analysis of Curlcurl-Conforming Elements on Rectangular Meshes.
Journal of Scientific Computing,
95(2).
http://doi.org/10.1007/s10915-023-02182-w
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/17068
