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.
| Original language | English |
|---|---|
| Article number | 116599 |
| Number of pages | 15 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 465 |
| Early online date | 24 Feb 2025 |
| DOIs | |
| Publication status | Published - Sept 2025 |
Keywords
- Cuboidal spectral element method
- Fourth-order div problem
- Graddiv-conforming elements
- Hierarchical basis functions
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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