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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics
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A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics

机译：不可压缩磁流体动力学具有精确无散度的混合有限元方法

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摘要

We introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem, in two and three dimensions. The velocity field is dis-cretized using divergence-conforming Brezzi-Douglas-Marini (BDM) elements and the magnetic field is approximated by curl-conforming Nedelec elements. The H~1-continuity of the velocity field is enforced by a DG approach. A central feature of the method is that it produces exactly divergence-free velocity approximations, and captures the strongest magnetic singularities. We prove that the energy norm error is convergent in the mesh size in general Lipschitz polyhedra under minimal regularity assumptions, and derive nearly optimal a priori error estimates for the two-dimensional case. We present a comprehensive set of numerical experiments, which indicate optimal convergence of the proposed method for two-dimensional as well as three-dimensional problems.
机译：我们引入和分析混合有限元方法，用于二维和三维二维静态不可压缩磁流体动力学问题的数值离散化。速度场使用发散一致性的Brezzi-Douglas-Marini（BDM）元素进行离散，磁场通过卷曲一致性的Nedelec元素进行近似。速度场的H〜1连续性是通过DG方法实现的。该方法的主要特点是，它可以产生完全无散度的速度近似值，并捕获最强的磁奇异性。我们证明了在最小规则性假设下，能量范数误差在一般Lipschitz多面体中的网格大小上是收敛的，并且针对二维情况得出了几乎最佳的先验误差估计。我们提出了一套完整的数值实验，它表明了针对二维和三维问题的拟议方法的最优收敛性。

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