Published

Distributional Finite Element curl div Complexes and Application to Quad Curl Problems

Long Chen, Xuehai Huang, and Chao Zhang

SIAM Journal on Numerical Analysis. 63 (3), 2025. DOI

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ABSTRACT:

The paper addresses the challenge of constructing conforming
finite element spaces for high-order differential operators in high
dimensions, with a focus on the curl div operator in three
dimensions. Tangential-normal continuity is introduced in order to
develop distributional finite element curl div complexes. The spaces
constructed are applied to discretize a quad curl problem,
demonstrating optimal order of convergence. Furthermore, a
hybridization technique is proposed, demonstrating its equivalence to
nonconforming finite elements and weak Galerkin methods.