论文标题
Cahn-Hilliard-Magneto-Hydrodynalnics问题的完全离散方案的错误分析
Error analysis of a fully discrete scheme for the Cahn-Hilliard-Magneto-hydrodynamics problem
论文作者
论文摘要
在本文中，我们分析了一般Cahn-Hilliard方程的完全离散的方案，再加上非稳态的磁磁动力学流量，该方程描述了两种不可分割的，不可压缩的和电动传导流体，具有不同的迁移率，流体粘度和磁性扩散。详细考虑了一种典型的完全离散的方案，该方案由符合有限元方法和基于方程能量的凸形分解的Euler半平整化离散化组成。我们证明我们的方案是无条件的能量稳定性，并获得了浓度场，化学电位，速度场，磁场和压力的一些最佳误差估计。提出了数值测试的结果，以验证收敛速率。
In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different mobilities, fluid viscosities and magnetic diffusivities. A typical fully discrete scheme, which is comprised of conforming finite element method and the Euler semi-implicit discretization based on a convex splitting of the energy of the equation is considered in detail. We prove that our scheme is unconditionally energy stability and obtain some optimal error estimates for the concentration field, the chemical potential, the velocity field, the magnetic field and the pressure. The results of numerical tests are presented to validate the rates of convergence.
