论文标题
不稳定不可压缩的磁性水力动力学方程的曲柄 - 尼古尔森leap-frog方案
A Crank-Nicolson leap-frog scheme for the unsteady incompressible magnetohydrodynamics equations
论文作者
论文摘要
本文介绍了不稳定不可压缩的磁性流体动力学（MHD）方程的曲柄 - 尼科尔森Leap-Frog（CNLF）方案。空间离散化采用了Galerkin有限元方法（FEM），时间离散化采用了线性项的CNLF方法，非线性项的半平移方法。第一步使用Stokes Style的方案，第二步采用了Crank-Nicolson外推方案，而其他方案则采用了CNLF方案。我们证明，当时间步长小于或等于正常数时，完全离散的方案是稳定的且收敛的。第二阶$ l^{2} $错误估计可以通过新颖的负标准技术得出。数值结果与我们的理论分析一致，这表明该方法具有最佳的收敛顺序。因此，该方案对于不同参数有效。
This paper presents a Crank-Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization employs the CNLF method for linear terms and the semi-implicit method for nonlinear terms. The first step uses Stokes style's scheme, the second step employs the Crank-Nicolson extrapolation scheme, and others apply the CNLF scheme. We testify that the fully discrete scheme is stable and convergent when the time step is less than or equal to a positive constant. The second order $L^{2}$ error estimates can be derived by a novel negative norm technique. The numerical results are consistent with our theoretical analysis, which indicates that the method has an optimal convergence order. Therefore, the scheme is effective for different parameters.
