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

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