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

ESAIM: M2AN, 42 6 (2008) 1065-1087

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

Yun‐Bo Yang and Yao‐Lin Jiang
Mathematical Methods in the Applied Sciences 43 (2) 750 (2020)
DOI: 10.1002/mma.5958

## 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

## 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

## 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

## 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

## Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system

Qianqian Ding, Xiaonian Long and Shipeng Mao
Applied Numerical Mathematics 157 522 (2020)
DOI: 10.1016/j.apnum.2020.06.018

## 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

## 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

## 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

## Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Qili Tang and Yunqing Huang
Applied Mathematics and Mechanics 43 (1) 141 (2022)
DOI: 10.1007/s10483-022-2802-7

## Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations

Ľubomír Baňas and Andreas Prohl
Mathematics of Computation 79 (272) 1957 (2010)
DOI: 10.1090/S0025-5718-10-02341-0

## 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

## 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

## 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

## 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

## Second order fully decoupled and unconditionally energy-stable finite element algorithm for the incompressible MHD equations

Jinjin Yang and Shipeng Mao
Applied Mathematics Letters 121 107467 (2021)
DOI: 10.1016/j.aml.2021.107467

## 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

## 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

## Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations

Weifeng Qiu and Ke Shi
Computers & Mathematics with Applications 80 (10) 2150 (2020)
DOI: 10.1016/j.camwa.2020.09.003

## 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 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

## 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

## A constrained transport divergence-free finite element method for incompressible MHD equations

Lingxiao Li, Donghang Zhang and Weiying Zheng
Journal of Computational Physics 428 109980 (2021)
DOI: 10.1016/j.jcp.2020.109980

## Well-Posedness and Finite Element Approximation for the Stationary Magneto-Hydrodynamics Problem with Temperature-Dependent Parameters

Hailong Qiu
Journal of Scientific Computing 85 (3) (2020)
DOI: 10.1007/s10915-020-01361-3

## Error Analysis of Euler Semi-implicit Scheme for the Nonstationary Magneto-hydrodynamics Problem with Temperature Dependent Parameters

Hailong Qiu
Journal of Scientific Computing 85 (2) (2020)
DOI: 10.1007/s10915-020-01357-z

## 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

## Temporal convergence analysis of an energy preserving projection method for a coupled magnetohydrodynamics equations

Rong An, Chao Zhang and Yuan Li
Journal of Computational and Applied Mathematics 386 113236 (2021)
DOI: 10.1016/j.cam.2020.113236

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

Xiaojuan Shen, Yunxia Wang and Zhiyong Si
Applied Mathematics and Computation 387 124488 (2020)
DOI: 10.1016/j.amc.2019.06.002

## A Convergent Finite Element Method for the Compressible Magnetohydrodynamics System

Qianqian Ding and Shipeng Mao
Journal of Scientific Computing 82 (1) (2020)
DOI: 10.1007/s10915-020-01129-9

## Second-order energy stable schemes for the new model of the Cahn-Hilliard-MHD equations

Rui Chen and Hui Zhang
Advances in Computational Mathematics 46 (6) (2020)
DOI: 10.1007/s10444-020-09822-x

## A Convergent Linearized Lagrange Finite Element Method for the Magneto-hydrodynamic Equations in Two-Dimensional Nonsmooth and Nonconvex Domains

Buyang Li, Jilu Wang and Liwei Xu
SIAM Journal on Numerical Analysis 58 (1) 430 (2020)
DOI: 10.1137/18M1205649

## 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

## Convergence of Fully Discrete Implicit and Semi-implicit Approximations of Singular Parabolic Equations

Sören Bartels and Michael Růžička
SIAM Journal on Numerical Analysis 58 (1) 811 (2020)
DOI: 10.1137/19M126551X

## Error Estimate of a Fully Discrete Finite Element Method for Incompressible Vector Potential Magnetohydrodynamic System

Qianqian Ding, Xiaonian Long and Shipeng Mao
Journal of Scientific Computing 88 (3) (2021)
DOI: 10.1007/s10915-021-01571-3

## 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

## Uniformly robust preconditioners for incompressible MHD system

Guo-Dong Zhang and Chuanjun Chen
Journal of Computational and Applied Mathematics 379 112914 (2020)
DOI: 10.1016/j.cam.2020.112914

## A mixed DG method and an HDG method for incompressible magnetohydrodynamics

Ke Shi and Weifeng Qiu
IMA Journal of Numerical Analysis 40 (2) 1356 (2020)
DOI: 10.1093/imanum/dry095

## 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 81 (3) 1678 (2019)
DOI: 10.1007/s10915-019-01059-1

## A Modular Grad-Div Stabilization for the 2D/3D Nonstationary Incompressible Magnetohydrodynamic Equations

Xiaoli Lu and Pengzhan Huang
Journal of Scientific Computing 82 (1) (2020)
DOI: 10.1007/s10915-019-01114-x

## Isogeometric analysis of the time-dependent incompressible MHD equations

J. S. Ahn and M. J. Bluck
International Journal of Computational Fluid Dynamics 34 (3) 226 (2020)
DOI: 10.1080/10618562.2020.1737680

## Unconditionally optimal convergence analysis of second-order BDF Galerkin finite element scheme for a hybrid MHD system

Yuan Li and Chunfang Zhai
Advances in Computational Mathematics 46 (5) (2020)
DOI: 10.1007/s10444-020-09815-w

## Multi-level mixed finite element algorithms for the stationary incompressible magneto-hydrodynamics equations

Hailong Qiu
Computers & Mathematics with Applications 86 33 (2021)
DOI: 10.1016/j.camwa.2021.01.011

## 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

## Robust preconditioners for incompressible MHD models

Yicong Ma, Kaibo Hu, Xiaozhe Hu and Jinchao Xu
Journal of Computational Physics 316 721 (2016)
DOI: 10.1016/j.jcp.2016.04.019

## 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

## Temporal error analysis of Euler semi-implicit scheme for the magnetohydrodynamics equations with variable density

Yuan Li and Rong An
Applied Numerical Mathematics 166 146 (2021)
DOI: 10.1016/j.apnum.2021.04.006

## 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

## Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields

Feng Bai, Daozhi Han, Xiaoming He and Xiaofeng Yang
Communications in Nonlinear Science and Numerical Simulation 85 105213 (2020)
DOI: 10.1016/j.cnsns.2020.105213

## OPTIMAL $H^1$ ERROR ANALYSIS OF A FRACTIONAL STEP FINITE ELEMENT SCHEME FOR A HYBRID MHD SYSTEM

Jingke Wu, Rong An and Yuan Li
Journal of Applied Analysis & Computation 11 (3) 1535 (2021)
DOI: 10.11948/20200277

## 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

## 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

Yinnian He, Xiaojing Dong and Xinlong Feng
Journal of Scientific Computing 90 (1) (2022)
DOI: 10.1007/s10915-021-01671-0

## Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Luigi C. Berselli, Alex Kaltenbach and Michael Růžička
Mathematical Models and Methods in Applied Sciences 31 (11) 2297 (2021)
DOI: 10.1142/S0218202521500494

## Fully Discrete Finite Element Approximation of the MHD Flow

Yinnian He, Guo-Dong Zhang and Jun Zou
Computational Methods in Applied Mathematics 22 (2) 357 (2022)
DOI: 10.1515/cmam-2021-0172

## 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

## Two-level Newton iterative method based on nonconforming finite element discretization for 2D/3D stationary MHD equations

Jiali Xu, Xinlong Feng and Haiyan Su
Computers & Fluids 238 105372 (2022)
DOI: 10.1016/j.compfluid.2022.105372

## Optimal error estimates of a Crank–Nicolson finite element projection method for magnetohydrodynamic equations

Cheng Wang, Jilu Wang, Zeyu Xia and Liwei Xu
ESAIM: Mathematical Modelling and Numerical Analysis 56 (3) 767 (2022)
DOI: 10.1051/m2an/2022020

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

Haiyan Su, Jiali Xu and Xinlong Feng
Entropy 24 (5) 587 (2022)
DOI: 10.3390/e24050587

## A Finite Element Algorithm for the Nonstationary Incompressible Magnetohydrodynamic System Based on a Correction Method

Pengzhan Huang
Mediterranean Journal of Mathematics 19 (3) (2022)
DOI: 10.1007/s00009-022-02027-0

## Error analysis of the second-order BDF finite element scheme for the thermally coupled incompressible magnetohydrodynamic system

Zheqian Tang and Rong An
Computers & Mathematics with Applications 118 110 (2022)
DOI: 10.1016/j.camwa.2022.05.014

## Solution of Steady Incompressible MHD Problems with Quasi-Least Square Method

Shahid Hussain, Shams ur Rahman, Suhail Abbas and Munawwar Ali Abbas
Inventions 7 (2) 40 (2022)
DOI: 10.3390/inventions7020040

## An optimal error estimate of the BDF-Galerkin FEM for the incompressible MHD system

Shuaijun Liu, Pengzhan Huang and Yinnian He
Journal of Mathematical Analysis and Applications 515 (2) 126460 (2022)
DOI: 10.1016/j.jmaa.2022.126460

## A vector penalty-projection approach for the time-dependent incompressible magnetohydrodynamics flows

Huimin Ma and Pengzhan Huang
Computers & Mathematics with Applications 120 28 (2022)
DOI: 10.1016/j.camwa.2022.06.019

## A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients

Qianqian Ding, Xiaonian Long and Shipeng Mao
Entropy 24 (7) 912 (2022)
DOI: 10.3390/e24070912

## Convergence analysis of a fully discrete finite element method for thermally coupled incompressible MHD problems with temperature-dependent coefficients

Qianqian Ding, Xiaonian Long and Shipeng Mao
ESAIM: Mathematical Modelling and Numerical Analysis 56 (3) 969 (2022)
DOI: 10.1051/m2an/2022028

## An effective second-order scheme for the nonstationary incompressible magnetohydrodynamics equations

Xiaojuan Shen, Yunqing Huang and Xiaojing Dong
Computers & Mathematics with Applications (2022)
DOI: 10.1016/j.camwa.2022.07.007

## Error estimates of H(div)-conforming method for nonstationary magnetohydrodynamic system

Qianqian Ding, Shipeng Mao and Jiaao Sun
Advances in Computational Mathematics 48 (5) (2022)
DOI: 10.1007/s10444-022-09964-0

## On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field

Yang Li and Bangwei She
SIAM Journal on Numerical Analysis 60 (4) 2182 (2022)
DOI: 10.1137/21M1431011

## Error analysis of a conservative finite element scheme for time-dependent inductionless MHD problem

Xiaonian Long, Qianqian Ding and Shipeng Mao
Journal of Computational and Applied Mathematics 419 114728 (2023)
DOI: 10.1016/j.cam.2022.114728

## Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations

Zhe Zhang, Haiyan Su and Xinlong Feng
Entropy 24 (8) 1159 (2022)
DOI: 10.3390/e24081159

## An optimally accurate second-order time-stepping algorithm for the nonstationary magneto-hydrodynamics equations

Hailong Qiu
Applied Numerical Mathematics 184 151 (2023)
DOI: 10.1016/j.apnum.2022.09.018

## Error Analysis of a PFEM Based on the Euler Semi-Implicit Scheme for the Unsteady MHD Equations

Kaiwen Shi, Haiyan Su and Xinlong Feng
Entropy 24 (10) 1395 (2022)
DOI: 10.3390/e24101395

## Optimal L2 error analysis of first-order Euler linearized finite element scheme for the 2D magnetohydrodynamics system with variable density

Chenyang Li and Yuan Li
Computers & Mathematics with Applications 128 96 (2022)
DOI: 10.1016/j.camwa.2022.10.013