Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations
Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations
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三维不可压缩MHD方程欧拉半隐式格式的无条件收敛
DOI：
10.1093/imanum/dru015
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发表时间：
2015-04-01
影响因子：
2.1
通讯作者：
He, Yinnian
中科院分区：
文献类型：
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作者：
He, Yinnian
本文考虑三维不可压缩磁流体动力学方程的初边值问题。我们首先在假设u，H是L-4（0，T;H-1（Ω）（3））中的元素的条件下建立解（u，p，H）的某些正则性结果。其次，我们考虑基于混合有限元方法的全离散一阶欧拉半隐格式。然后利用负范数技巧得到了该格式的L-2-无条件收敛性。
In this paper, we consider the initial-boundary value problem for the three-dimensional incompressible magnetohydrodynamic equations. We first establish certain regularity results for the solution (u, p, H) under the assumption that u, H is an element of L-4(0, T;H-1 (Omega)(3)). Next, we consider the fully discrete first-order Euler semi-implicit scheme based on the mixed finite element method. Then we obtain the L-2-unconditional convergence of this scheme by using the negative norm technique.