Graddiv-conforming spectral element method for fourth-order div problems

Yang Han; Ping Lin; Lixiu Wang; Qian Zhang

doi:10.1016/j.cam.2025.116599

Graddiv-conforming spectral element method for fourth-order div problems

Yang Han, Ping Lin, Lixiu Wang (Lead / Corresponding author), Qian Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1016/j.cam.2025.116599
Publication status	E-pub ahead of print - 24 Feb 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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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.",

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AU - Lin, Ping

AU - Wang, Lixiu

AU - Zhang, Qian

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AB - 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.

KW - Cuboidal spectral element method

KW - Fourth-order div problem

KW - Graddiv-conforming elements

KW - Hierarchical basis functions

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DO - 10.1016/j.cam.2025.116599

M3 - Article

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JO - Journal of Computational and Applied Mathematics

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M1 - 116599

ER -

Graddiv-conforming spectral element method for fourth-order div problems

Abstract

Keywords

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