A semi-discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations

作者：Si, Zhiyong^*; Liu, Cui; Wang, Yunxia

来源：Mathematical Methods in the Applied Sciences, 2017, 40(11): 4179-4196.

DOI：10.1002/mma.4296

• semi-discrete defect correction method
• finite element method
• unsteady incompressible MHD equations
• stability analysis
• convergence analysis

In this report, we give a semi-discrete defect correction finite element method for the unsteady incompressible magnetohydrodynamics equations. The defect correction method is an iterative improvement technique for increasing the accuracy of a numerical solution without applying a grid refinement. Firstly, the nonlinear magnetohydrodynamics equations is solved with an artificial viscosity term. Then, the numerical solutions are improved on the same grid by a linearized defect-correction technique. Then, we give the numerical analysis including stability analysis and error analysis. The numerical analysis proves that our method is stable and has an optimal convergence rate. In order to show the effect of our method, some numerical results are shown.

• 出版日期2017-7-30
• 单位河南理工大学