论文标题
基于电荷保守的有限元法的固定热耦合无感应MHD系统的耦合迭代分析
Coupled iterative analysis for the stationary thermally coupled inductionless MHD system based on charge-conservative finite element method
论文作者
论文摘要
本文主要考虑基于Lipschitz域中电荷保守的有限元近似的三个迭代，用于固定的热耦合无感应MHD方程。基于杂化有限元方法，稳定的速度压力有限元元素对离散了流体动力学的未知数，并且电流密度以及电势同样由$ \ boldsymbol {h}（h}（\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\ boldsymbol {div}，\^2（）由于方程的强非线性，我们介绍了三种耦合的迭代方法，即Stokes，Newton和Oseen迭代以及在不同独特条件下的收敛和稳定性。事实证明，速度，电流密度，温度和压力的误差估计不取决于潜力。理论分析通过给定的数值结果验证，对于提出的方法，证明了适用性和有效性。
This paper mainly considers three iterations based on charge-conservative finite element approximation in Lipschitz domain for the stationary thermally coupled inductionless MHD equations. Based on the hybrid finite element method, the unknowns of hydrodynamic are discretized by the stable velocity-pressure finite element pair, and the current density along with electric potential are similarly discretized by the comforming finite element pair in $\boldsymbol{H}(\boldsymbol{div}, Ω)\times L^2(Ω)$. And on account of the strong nonlinearity of the equations, we present three coupled iterative methods, namely, the Stokes, Newton and Oseen iteration and the convergence and stability under different uniqueness conditions are analyzed strictly. It is proved especially that the error estimates of velocity, current density, temperature and pressure do not depend on potential. The theoretical analysis is validated by the given numerical results, and for the proposed methods, the applicability and effectiveness are demonstrated.
