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A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations

A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations

Year:    2025

Author:    Ruo Li, Qicheng Liu, Shuhai Zhao

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 517–537

Abstract

We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to control the divergence of the field. The approximation space for the original variable is constructed by patch reconstruction with exactly one degree of freedom per element in each dimension and the auxiliary variable is approximated by the piecewise constant space. We prove the optimal convergence rate under the energy norm and also suboptimal $L^2$ convergence using a duality approach. Numerical results are provided to verify the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2024-0086

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 517–537

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Quad-Curl problem mixed formulation patch reconstruction.

Author Details

Ruo Li

Qicheng Liu

Shuhai Zhao