TY - JOUR
T1 - Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations
AU - Dong , Xiaojing
AU - He , Yinnian
JO - Journal of Computational Mathematics
VL - 1
SP - 49
EP - 70
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2201-m2021-0140
UR - https://global-sci.org/intro/article_detail/jcm/22152.html
KW - Partition of unity method, Local and parallel algorithm, Finite element
method, Iteration methods, Magnetohydrodynamics.
AB - <p style="text-align: justify;">By combination of iteration methods with the partition of unity method (PUM), some
finite element parallel algorithms for the stationary incompressible magnetohydrodynamics
(MHD) with different physical parameters are presented and analyzed. These algorithms
are highly efficient. At first, a global solution is obtained on a coarse grid for all approaches
by one of the iteration methods. By parallelized residual schemes, local corrected solutions
are calculated on finer meshes with overlapping sub-domains. The subdomains can be
achieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformly
stable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.</p>