论文标题
不可压缩的MHD方程的约束无差异有限元法
A constrained transport divergence-free finite element method for Incompressible MHD equations
论文作者
论文摘要
在本文中，我们研究了三维不可压缩电阻磁性水力动力学方程的有限元方法，其中速度，电流密度和磁诱导不含差异。希望离散的解决方案还应完全满足无差异条件，尤其是对于动量方程式。受限制运输方法的启发，我们设计了一种可以实现目标的新的稳定混合有限元方法。我们还证明了离散解决方案的适当性。为了求解所得的线性代数方程，我们提出了具有增强拉格朗日块预处理的GMRE求解器。通过数值实验，我们验证理论结果并证明离散求解器相对于自由度的数量
In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the discrete solutions should also satisfy divergence-free conditions exactly especially for the momentum equations. Inspired by constrained transport method,we devise a new stable mixed finite element method that can achieve the goal. We also prove the well-posedness of the discrete solutions. To solve the resulting linear algebraic equations, we propose a GMRES solver with an augmented Lagrangian block preconditioner. By numerical experiments, we verify the theoretical results and demonstrate the quasi-optimality of the discrete solver with respect to the number of degrees of freedom
