A semi‐discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations |
| |
| Authors: | Zhiyong Si Cui Liu Yunxia Wang |
| |
| Affiliation: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China;2. School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, China |
| |
| Abstract: | 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. Copyright © 2017 John Wiley & Sons, Ltd. |
| |
| Keywords: | semi‐discrete defect correction method finite element method unsteady incompressible MHD equations stability analysis convergence analysis subclass 76D05 35Q30 65M60 65N30 |
|
|
