Spurious solutions for high-order curl problems
Document Type
Article
Publication Date
5-2023
Department
Department of Mathematical Sciences
Abstract
We investigate numerical solutions of high-order problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spurious solutions, while mixed formulations with finite elements in complexes solve the problems correctly. To explain the numerical results, we clarify the cohomological structures in high-order problems by relating the partial differential equations to the Hodge-Laplacian boundary problems of the complexes.
Publication Title
IMA Journal of Numerical Analysis
Recommended Citation
Hu, K.,
Zhang, Q.,
Han, J.,
Wang, L.,
&
Zhang, Z.
(2023).
Spurious solutions for high-order curl problems.
IMA Journal of Numerical Analysis,
43(3), 1422-1449.
http://doi.org/10.1093/imanum/drac024
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/17278