A TWO-LEVEL DISCRETIZATION METHOD FOR THE STATIONARY MHD EQUATIONS
A TWO-LEVEL DISCRETIZATION METHOD FOR THE STATIONARY MHD EQUATIONS
复制标题
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
W. Layton;A. Meir;P. Schmidt
中科院分区：
文献类型：
--
作者：
W. Layton;A. Meir;P. Schmidt
我们描述和分析了一个两级有限元方法离散方程的静态，粘性，不可压缩磁流体动力学（或MHD）。这些方程模拟了在电磁场存在下导电流体的流动，出现在等离子体物理学和液态金属技术以及电子物理学和天文学中。我们对待物理现实（“非理想”）的边界条件下，占周围介质的流体的电磁相互作用的方程。建议的算法涉及解决一个小的，非线性问题的粗网格，然后一个大的，线性问题的细网格。我们证明了算法的适定性和小数据假设下的最佳误差估计。
We describe and analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics (or MHD). These equations, which model the flow of electrically conducting fluids in the presence of electromagnetic fields, arise in plasma physics and liquid-metal technology as well as in geophysics and astronomy. We treat the equations under physically realistic ("nonideal") boundary conditions that account for the electromagnetic interaction of the fluid with the surrounding media. The suggested algorithm involves solving a small, nonlinear problem on a coarse mesh and then one large, linear problem on a fine mesh. We prove well-posedness of the algorithm and optimal error estimates under a small-data assumption.