TY - JOUR
T1 - Stability and Convergence of Stabilized Finite Volume Iterative Methods for Steady Incompressible MHD Flows with Different Viscosities
AU - Chu , Xiaochen
AU - Chen , Chuanjun
AU - Zhang , Tong
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 361
EP - 397
PY - 2023
DA - 2023/04
SN - 13
DO - http://doi.org/10.4208/eajam.2022-204.241022
UR - https://global-sci.org/intro/article_detail/eajam/21653.html
KW - Incompressible MHD equation, finite volume method, $L^2$-projection, iterative scheme.
AB - <p style="text-align: justify;">Three finite volume iterative schemes for steady incompressible magnetohydrodynamic problems are studied. The theoretical analysis of finite volume methods is
more challenging than that of finite element methods because of the presence of a trilinear
form and the difficulties with the treatment of nonlinear terms. Nevertheless, we prove
the uniform stability of the methods and establish error estimates. It is worth noting
that the Newton iterative scheme converges exponentially under viscosity related requirements, while the Oseen iterative method is unconditionally stable and convergent
under the uniqueness condition. Some numerical examples confirm the theoretical findings and demonstrate a good performance of the methods under consideration.</p>