Graddiv-conforming spectral element method for fourth-order div problems
Document Type
Article
Publication Date
9-2025
Department
Department of Mathematical Sciences
Abstract
This paper introduces a novel numerical method to solve fourth-order div problems using graddiv-conforming spectral elements on cuboidal meshes. We start by determining the continuity requirements for graddiv-conforming spectral elements, followed by constructing these elements using generalized Jacobi polynomials and the Piola transformation. The resulting basis functions exhibit a hierarchical structure, making them easily extendable to higher orders. We apply these graddiv-conforming spectral elements to solve the fourth-order div problem and present numerical examples to verify both the efficiency and effectiveness of the method.
Publication Title
Journal of Computational and Applied Mathematics
Recommended Citation
Han, Y.,
Lin, P.,
Wang, L.,
&
Zhang, Q.
(2025).
Graddiv-conforming spectral element method for fourth-order div problems.
Journal of Computational and Applied Mathematics,
465.
http://doi.org/10.1016/j.cam.2025.116599
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/1495