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## Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system

ESAIM: M2AN, 42 6 (2008) 1065-1087
Published online: 2008-08-12

## A parallel finite element algorithm for nonstationary incompressible magnetohydrodynamics equations

Qili Tang
International Journal of Numerical Methods for Heat & Fluid Flow 28 (7) 1579 (2018)
DOI: 10.1108/HFF-06-2017-0251

## Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations

Dongyang Shi and Zhiyun Yu
Journal of Applied Mathematics 2012 1 (2012)
DOI: 10.1155/2012/825609

## Error analysis of first-order projection method for time-dependent magnetohydrodynamics equations

Rong An and Yuan Li
Applied Numerical Mathematics 112 167 (2017)
DOI: 10.1016/j.apnum.2016.10.010

## Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations

Guo-Dong Zhang and Yinnian He
International Journal of Numerical Methods for Heat & Fluid Flow 25 (8) 1912 (2015)
DOI: 10.1108/HFF-08-2014-0257

## Local and Parallel Finite Element Algorithm Based on Oseen-Type Iteration for the Stationary Incompressible MHD Flow

Qili Tang and Yunqing Huang
Journal of Scientific Computing 70 (1) 149 (2017)
DOI: 10.1007/s10915-016-0246-1

## Stability and Error Analysis for the First-Order Euler Implicit/Explicit Scheme for the 3D MHD Equations

Jinjin Yang and Yinnian He
International Journal of Computational Methods 15 (01) 1750077 (2018)
DOI: 10.1142/S0219876217500773

## Numerical analysis of the Crank-Nicolson extrapolation time discrete scheme for magnetohydrodynamics flows

Yuhong Zhang, Yanren Hou and Li Shan
Numerical Methods for Partial Differential Equations 31 (6) 2169 (2015)
DOI: 10.1002/num.21989

## Two-Level Coupled and Decoupled Parallel Correction Methods for Stationary Incompressible Magnetohydrodynamics

Guo-Dong Zhang, Yan Zhang and Yinnian He
Journal of Scientific Computing 65 (3) 920 (2015)
DOI: 10.1007/s10915-015-9994-6

## A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics

Chen Greif, Dan Li, Dominik Schötzau and Xiaoxi Wei
Computer Methods in Applied Mechanics and Engineering 199 (45-48) 2840 (2010)
DOI: 10.1016/j.cma.2010.05.007

## A rotational pressure-correction projection methods for unsteady incompressible Magnetohydrodynamics equations

Xiaojuan Shen, Yunxia Wang and Zhiyong Si
Applied Mathematics and Computation (2019)
DOI: 10.1016/j.amc.2019.06.002

## Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

Guo-Dong Zhang and Yinnian He
Computers & Mathematics with Applications 69 (12) 1390 (2015)
DOI: 10.1016/j.camwa.2015.03.019

## Stable finite element methods preserving $$\nabla \cdot \varvec{B}=0$$ ∇ · B = 0 exactly for MHD models

Kaibo Hu, Yicong Ma and Jinchao Xu
Numerische Mathematik 135 (2) 371 (2017)
DOI: 10.1007/s00211-016-0803-4

## A priori estimates and optimal finite element approximation of the MHD flow in smooth domains

Yinnian He and Jun Zou
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 181 (2018)
DOI: 10.1051/m2an/2018006

## Second order unconditionally convergent and energy stable linearized scheme for MHD equations

Guo-Dong Zhang, Jinjin Yang and Chunjia Bi
Advances in Computational Mathematics 44 (2) 505 (2018)
DOI: 10.1007/s10444-017-9552-x

## Streamline diffusion finite element method for stationary incompressible magnetohydrodynamics

Guo-Dong Zhang, Yinnian He and Yan Zhang
Numerical Methods for Partial Differential Equations 30 (6) 1877 (2014)
DOI: 10.1002/num.21882

## On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Santiago Badia, Ramon Codina and Ramon Planas
Journal of Computational Physics 234 399 (2013)
DOI: 10.1016/j.jcp.2012.09.031

## Asymmetric and moving-frame approaches to MHD equations

Bin Tao Cao
Acta Mathematica Sinica, English Series 28 (1) 1 (2012)
DOI: 10.1007/s10114-012-0503-7

## A fully divergence-free finite element method for magnetohydrodynamic equations

Ralf Hiptmair, Lingxiao Li, Shipeng Mao and Weiying Zheng
Mathematical Models and Methods in Applied Sciences 28 (04) 659 (2018)
DOI: 10.1142/S0218202518500173

## Decoupled, semi-implicit scheme for a coupled system arising in magnetohydrodynamics problem

Yuan Li, Yanjie Ma and Rong An
Applied Numerical Mathematics 127 142 (2018)
DOI: 10.1016/j.apnum.2018.01.005

## Partitioned time-stepping scheme for an MHD system with temperature-dependent coefficients

S S Ravindran
IMA Journal of Numerical Analysis 39 (4) 1860 (2019)
DOI: 10.1093/imanum/dry037

## Second-order semi-implicit Crank-Nicolson scheme for a coupled magnetohydrodynamics system

Yuan Li and Xuelan Luo
Applied Numerical Mathematics 145 48 (2019)
DOI: 10.1016/j.apnum.2019.06.001

## A least squares finite element method using Elsasser variables for magnetohydrodynamic equations

Eunjung Lee, Heonkyu Ha and Sang Dong Kim
Journal of Computational and Applied Mathematics 346 599 (2019)
DOI: 10.1016/j.cam.2018.06.038

## An Extrapolated Second Order Backward Difference Time-Stepping Scheme for the Magnetohydrodynamics System

S. S. Ravindran
Numerical Functional Analysis and Optimization 37 (8) 990 (2016)
DOI: 10.1080/01630563.2016.1181651

## Error analysis of a fractional-step method for magnetohydrodynamics equations

Rong An and Can Zhou
Journal of Computational and Applied Mathematics 313 168 (2017)
DOI: 10.1016/j.cam.2016.09.005

## Decoupled schemes for unsteady MHD equations. I. time discretization

Guo-Dong Zhang and Yinnian He
Numerical Methods for Partial Differential Equations 33 (3) 956 (2017)
DOI: 10.1002/num.22132

## On an efficient second order backward difference Newton scheme for MHD system

Jinjin Yang, Yinnian He and Guodong Zhang
Journal of Mathematical Analysis and Applications 458 (1) 676 (2018)
DOI: 10.1016/j.jmaa.2017.09.024

## Stability and convergence analysis of a Crank–Nicolson leap-frog scheme for the unsteady incompressible Navier–Stokes equations

Qili Tang and Yunqing Huang
Applied Numerical Mathematics 124 110 (2018)
DOI: 10.1016/j.apnum.2017.09.012

## A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows

Jinjin Yang, Shipeng Mao, Xiaoming He, Xiaofeng Yang and Yinnian He
Computer Methods in Applied Mechanics and Engineering 356 435 (2019)
DOI: 10.1016/j.cma.2019.07.022

## A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part I: Convergence

Lingxiao Li, Mingjiu Ni and Weiying Zheng
SIAM Journal on Scientific Computing 41 (4) B796 (2019)
DOI: 10.1137/17M1160768

## Analysis of coupling iterations based on the finite element method for stationary magnetohydrodynamics on a general domain

Guo-Dong Zhang, Yinnian He and Di Yang
Computers & Mathematics with Applications 68 (7) 770 (2014)
DOI: 10.1016/j.camwa.2014.07.025

## A semi-implicit energy conserving finite element method for the dynamical incompressible magnetohydrodynamics equations

Computer Methods in Applied Mechanics and Engineering 346 982 (2019)
DOI: 10.1016/j.cma.2018.09.037

## A Decoupled, Linear and Unconditionally Energy Stable Scheme with Finite Element Discretizations for Magneto-Hydrodynamic Equations

Guo-Dong Zhang, XiaoMing He and XiaoFeng Yang
Journal of Scientific Computing (2019)
DOI: 10.1007/s10915-019-01059-1

## Optimal convergence analysis of Crank–Nicolson extrapolation scheme for the three-dimensional incompressible magnetohydrodynamics

Xiaojing Dong and Yinnian He
Computers & Mathematics with Applications 76 (11-12) 2678 (2018)
DOI: 10.1016/j.camwa.2018.08.060

## Convergence analysis of an unconditionally energy stable projection scheme for magneto-hydrodynamic equations

Xiaofeng Yang, Guo-Dong Zhang and Xiaoming He
Applied Numerical Mathematics 136 235 (2019)
DOI: 10.1016/j.apnum.2018.10.013

## Error correction iterative method for the stationary incompressible MHD flow

Yun‐Bo Yang and Yao‐Lin Jiang
Mathematical Methods in the Applied Sciences (2019)
DOI: 10.1002/mma.5958

## Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations

Guo-Dong Zhang, Xiaoming He and Xiaofeng Yang
Journal of Computational and Applied Mathematics 369 112636 (2020)
DOI: 10.1016/j.cam.2019.112636

## Numerical Analysis of an Artificial Compression Method for Magnetohydrodynamic Flows at Low Magnetic Reynolds Numbers

Yao Rong, William Layton and Haiyun Zhao
Journal of Scientific Computing 76 (3) 1458 (2018)
DOI: 10.1007/s10915-018-0670-5

## The Arrow–Hurwicz iterative finite element method for the stationary magnetohydrodynamics flow

Yun-Bo Yang, Yao-Lin Jiang and Qiong-Xiang Kong
Applied Mathematics and Computation 356 347 (2019)
DOI: 10.1016/j.amc.2018.10.050