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Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
Haiyan Su1, Jiali Xu1, Xinlong Feng1
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.
Entropy (Basel, Switzerland)
|May 28, 2022
Summary
This study introduces novel two-level iterative methods for solving magnetohydrodynamics (MHD) equations. These methods, utilizing nonconforming finite elements, demonstrate stability and effectiveness for complex fluid dynamics simulations.
Area of Science:
- Computational fluid dynamics
- Numerical analysis
- Magnetohydrodynamics (MHD)
Background:
- Incompressible magnetohydrodynamics (MHD) equations present significant numerical challenges.
- Existing iterative methods require refinement for efficiency and stability.
Purpose of the Study:
- To develop and analyze novel two-level iterative methods for solving 2D/3D stationary incompressible MHD equations.
- To investigate the performance of these methods under various uniqueness conditions.
Main Methods:
- Application of nonconforming finite element methods.
- Implementation of two-level iterative schemes with coarse and fine grid corrections.
- Analysis of a one-level Oseen iterative method under weak uniqueness.
Main Results:
- Rigorous stability and error estimates were established for the proposed methods.
- The two-level iterative approaches demonstrated effectiveness.
- Numerical examples validated the theoretical findings.
Conclusions:
- The developed two-level iterative methods are stable and effective for solving MHD equations.
- The theoretical analysis and numerical results confirm the proposed methods' validity.
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