TY - JOUR
T1 - A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations
AU - Li , Ruo
AU - Liu , Qicheng
AU - Zhao , Shuhai
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 517
EP - 537
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2024-0086
UR - https://global-sci.org/intro/article_detail/aamm/23732.html
KW - Quad-Curl problem, mixed formulation, patch reconstruction.
AB - <p style="text-align: justify;">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.</p>