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

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