论文标题
对不可压缩磁性流动力学的混合有限元方法的新分析
New analysis of Mixed finite element methods for incompressible Magnetohydrodynamics
论文作者
论文摘要
该论文着重于对一类混合FEM的新误差分析，用于固定的不可压缩磁性水力动力学，并具有标准的INF-SUP稳定速度压力空间对与Navier-Stokes方程和Nédélec的边缘元素用于磁场。在过去的几十年中，这些方法已被广泛用于各种数值模拟中，而由于系统的强耦合以及分析中低阶Nédélec的边缘近似值，现有分析并不是最佳的。根据新修改的麦克斯韦投影，我们建立了新的和最佳的错误估计。特别是，我们证明了基于常用的泰勒 - 霍德/最低级nédélec的边缘元素的方法有效，该方法为数值速度提供了二阶精度。介绍了凸和非凸多边形结构域中该问题的两个数值示例。数值结果证实了我们的理论分析。
The paper focuses on a new error analysis of a class of mixed FEMs for stationary incompressible magnetohydrodynamics with the standard inf-sup stable velocity-pressure space pairs to Navier-Stokes equations and the Nédélec's edge element for the magnetic field. The methods have been widely used in various numerical simulations in the last several decades, while the existing analysis is not optimal due to the strong coupling of system and the pollution of the lower-order Nédélec's edge approximation in analysis. In terms of a newly modified Maxwell projection we establish new and optimal error estimates. In particular, we prove that the method based on the commonly-used Taylor-Hood/lowest-order Nédélec's edge element is efficient and the method provides the second-order accuracy for numerical velocity. Two numerical examples for the problem in both convex and nonconvex polygonal domains are presented. Numerical results confirm our theoretical analysis.
