TY - JOUR
T1 - Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium
AU - Liu , Nuodi
AU - Chen , Yanping
AU - Huang , Yunqing
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 371
EP - 396
PY - 2024
DA - 2024/04
SN - 14
DO - http://doi.org/10.4208/eajam.2022-293.010923
UR - https://global-sci.org/intro/article_detail/eajam/23067.html
KW - Maxwell’s equations, two-grid method, Raviart-Thomas-Nédélec mixed finite elements, postprocessing technique.
AB - <p style="text-align: justify;">A two-grid method (TGM) for the time-dependent Maxwell’s equations in
Cole-Cole dispersive media with a fractional time derivative term is proposed. We employ the lowest Raviart-Thomas-Nédélec mixed finite elements to discrete the space. It
is known that for these type of Nédélec edge finite elements, the standard TGM cannot be applied directly. Therefore, we modified the traditional TGM, and the discrete
process can be divided into two steps. Firstly, we get the rough discrete solutions on
the coarse mesh. At the same time, superconvergence results can be obtained by using
a post-processing technique. Secondly, the superconvergent solutions on the coarse grid
are added on the fine mesh as a correction, and the optimal error estimates could be
obtained accordingly. Finally, the numerical experiments can verify that the theoretical
results are correct and reasonable.</p>