H(curl2)-conforming triangular spectral element method for quad-curl problems
Document Type
Article
Publication Date
5-15-2025
Department
Department of Mathematical Sciences
Abstract
In this paper, we consider the H(curl2)-conforming triangular spectral element method to solve the quad-curl problems. We first explicitly construct the H(curl2)-conforming elements on triangles through the contravariant transform and the affine mapping from the reference element to physical elements. These constructed elements possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. We then establish H(curl2)-conforming triangular spectral element spaces and the corresponding mixed formulated spectral element approximation scheme for the quad-curl problems and related eigenvalue problems. Subsequently, we present the best spectral element approximation theory in H(curl2;Ω)-seminorms. Notably, the degrees of polynomials in the kernel space solely impact the convergence rate of the (L2(Ω))2-norm of uh, without affecting the semi-norm of H(curl;Ω) and H(curl2;Ω). This observation enables us to derive eigenvalue approximations from either the upper or lower side by selecting different degrees of polynomials for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.
Publication Title
Journal of Computational and Applied Mathematics
Recommended Citation
Wang, L.,
Li, H.,
Zhang, Q.,
&
Zhang, Z.
(2025).
H(curl2)-conforming triangular spectral element method for quad-curl problems.
Journal of Computational and Applied Mathematics,
459.
http://doi.org/10.1016/j.cam.2024.116362
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1349