Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations

Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the iterations on a coarse grid and corr...

Full description

Saved in:
Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 24; no. 5; p. 587
Main Authors Su, Haiyan, Xu, Jiali, Feng, Xinlong
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 22.04.2022
MDPI
Subjects
Algorithms
error estimate
Finite element method
incompressible MHD equations
Iterative methods
Magnetic fields
Mathematical analysis
nonconforming finite element
Reynolds number
stability
two-level method
Uniqueness
Velocity
error estimate
nonconforming finite element
incompressible MHD equations
two-level method
stability
Online AccessGet full text

Cover

More Information
Summary:Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1099-4300
1099-4300
DOI:10.3390/e24050587