Uniform Stability and Convergence with Respect to $$(\nu , \mu , s, 1-\sigma )$$ of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations

2021 ◽  
Vol 90 (1) ◽  
Author(s):  
Yinnian He ◽  
Xiaojing Dong ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Uniform Stability ◽  
Mhd Equations ◽  
Stability And Convergence

Stability and convergence of iterative finite element methods for the thermally coupled incompressible MHD flow

2020 ◽  
Vol 30 (12) ◽  
pp. 5103-5141
Author(s):  
Jinting Yang ◽  
Tong Zhang
Keyword(s):  
Finite Element ◽  
Iterative Method ◽  
Bounded Domain ◽  
Finite Element Methods ◽  
Mhd Flow ◽  
Mhd Equations ◽  
Stability And Convergence ◽  
Physical Parameters ◽  
Content Type ◽  
Incompressible Mhd

Purpose The purpose of this paper is to propose three iterative finite element methods for equations of thermally coupled incompressible magneto-hydrodynamics (MHD) on 2D/3D bounded domain. The detailed theoretical analysis and some numerical results are presented. The main results show that the Stokes iterative method has the strictest restrictions on the physical parameters, and the Newton’s iterative method has the higher accuracy and the Oseen iterative method is stable unconditionally. Design/methodology/approach Three iterative finite element methods have been designed for the thermally coupled incompressible MHD flow on 2D/3D bounded domain. The Oseen iterative scheme includes solving a linearized steady MHD and Oseen equations; unconditional stability and optimal error estimates of numerical approximations at each iterative step are established under the uniqueness condition. Stability and convergence of numerical solutions in Newton and Stokes’ iterative schemes are also analyzed under some strong uniqueness conditions. Findings This work was supported by the NSF of China (No. 11971152). Originality/value This paper presents the best choice for solving the steady thermally coupled MHD equations with different physical parameters.

scholarly journals Some Second-Order σ Schemes Combined with an H1-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 187
Author(s):  
Yaxin Hou ◽  
Cao Wen ◽  
Hong Li ◽  
Yang Liu ◽  
Zhichao Fang ◽  
...  
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Mixed Finite Element ◽  
Second Order ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
The Stability ◽  
High Order Time ◽  
Distributed Order ◽  
Convergence Of The Scheme

In this article, some high-order time discrete schemes with an H 1 -Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order σ schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.

A New Method for Computing Eigenpairs of a Finite Element Structure

2014 ◽  
Vol 590 ◽  
pp. 672-676
Author(s):  
Ping Liang ◽  
Yu Hang Zhang ◽  
Jun Wei ◽  
Bing Yu
Keyword(s):  
Dynamical System ◽  
Finite Element ◽  
New Method ◽  
Stability And Convergence ◽  
Power Method ◽  
Value Iteration ◽  
Eigenvalues And Eigenvectors ◽  
Simpler Algorithm ◽  
Distribution Of Eigenvalues ◽  
D Value

Based on the weighted inverse topological change method and by introducing a new concept of mass submembers, a dynamical system can be transformed into a static one. Using the properties of the weighted D value, i.e. the weighted D value decreases monotonously with parameter λ increasing; a new method called the weighted D value iteration method is presented for computing the eigenpairs (eigenvalues and eigenvectors). Using this method a series of eigenpairs of a finite element structure can be obtained. It has a merit of simpler algorithm and less computation efforts. Not as the power method, its stability and convergence rate does not depend on the distribution of eigenvalues, and convergent quickly. An example is given to demonstrate the valid of this method.

Sign in / Sign up

Export Citation Format

Share Document