A Nonconforming Finite Element Method for the Quad-Curl Hodge-Laplacian Problem in Two Dimensions
Document Type
Article
Publication Date
3-24-2025
Department
Department of Mathematical Sciences
Abstract
In this paper, we introduce an H1-nonconforming vector-valued finite element whose rot has H1-conformity. This element yields a nonconforming interior-penalty finite element method for the primal formulation of the quad-curl Hodge-Laplacian problem. Contrasting with conforming methods based on the primal formulation, our method effectively avoids spurious solutions on non-convex polygonal domains. We establish rigorous error estimates for the method in both the energy norm and the L2 norm, under graded meshes with various grading parameters. Numerical examples are used to verify our theoretical findings.
Publication Title
Journal of Scientific Computing
Recommended Citation
Tong, S.,
Zhai, Q.,
&
Zhang, Q.
(2025).
A Nonconforming Finite Element Method for the Quad-Curl Hodge-Laplacian Problem in Two Dimensions.
Journal of Scientific Computing,
103(42).
http://doi.org/10.1007/s10915-025-02858-5
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1512
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The work of Zhai was supported by the National Natural Science Foundation of China (No. 12271208). The work of Zhang was supported by Simons Foundation, USA, MPS-TSM-00007606.