Mixed finite element methods for stationary incompressible magneto-hydrodynamics
Mixed finite element methods for stationary incompressible magneto-hydrodynamics
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DOI：
10.1007/s00211-003-0487-4
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发表时间：
2004-02-01
影响因子：
2.1
通讯作者：
Schötzau, D
中科院分区：
文献类型：
--
作者：
Schötzau, D
介绍了一种新的稳态不可压缩磁流体动力学方程的混合变分形式，并对其进行了分析。该配方是基于卷曲符合Sobolev空间的磁性变量，并被证明是适定的（可能是非凸的）Lipschitz多面体。提出了一种有限元近似，其中流体动力学未知数由标准的inf-sup稳定的速度-压力空间对和磁的混合方法使用Nederian的第一类元素的离散。进行了误差分析表明，所提出的有限元近似导致准最佳的误差范围内的网格大小。
A new mixed variational formulation of the equations of stationary incompressible magneto-hydrodynamics is introduced and analyzed. The formulation is based on curl-conforming Sobolev spaces for the magnetic variables and is shown to be well-posed in (possibly non-convex) Lipschitz polyhedra. A finite element approximation is proposed where the hydrodynamic unknowns are discretized by standard inf-sup stable velocity-pressure space pairs and the magnetic ones by a mixed approach using Nedelec's elements of the first kind. An error analysis is carried out that shows that the proposed finite element approximation leads to quasi-optimal error bounds in the mesh-size.