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.