Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations

Cheng Wang; Jilu Wang; Steven M. Wise; Zeyu Xia; Liwei Xu

doi:10.1016/j.cam.2023.115409

Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations

Cheng Wang
, Jilu Wang
, Steven M. Wise
, Zeyu Xia
, Liwei Xu^*

^*Corresponding author for this work

University of Massachusetts Dartmouth
Harbin Institute of Technology
University of Tennessee
University of Electronic Science and Technology of China

Research output: Contribution to journal › Article › peer-review

57 Scopus citations

Abstract

In this paper we propose and analyze a temporally second-order accurate numerical scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations. The scheme is based on a modified Crank–Nicolson-type approximation for the time discretization and a mixed finite element method for the spatial discretization. The modified Crank–Nicolson approximation enables us to carry out the mass conservation and the energy stability analysis. Error estimates are derived for the phase field in the L_τ^∞(0,T;H¹) norm, and for the velocity and the magnetic fields in the L_τ^∞(0,T;L²) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.

Original language	English
Article number	115409
Journal	Journal of Computational and Applied Mathematics
Volume	436
DOIs	https://doi.org/10.1016/j.cam.2023.115409
State	Published - 15 Jan 2024
Externally published	Yes

Keywords

CH-MHD system
Crank–Nicolson method
Error estimates
Finite element approximation
Unconditional energy stability
Unique solvability

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10.1016/j.cam.2023.115409

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title = "Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn{\textendash}Hilliard-Magnetohydrodynamics system of equations",

abstract = "In this paper we propose and analyze a temporally second-order accurate numerical scheme for the Cahn{\textendash}Hilliard-Magnetohydrodynamics system of equations. The scheme is based on a modified Crank{\textendash}Nicolson-type approximation for the time discretization and a mixed finite element method for the spatial discretization. The modified Crank{\textendash}Nicolson approximation enables us to carry out the mass conservation and the energy stability analysis. Error estimates are derived for the phase field in the Lτ∞(0,T;H1) norm, and for the velocity and the magnetic fields in the Lτ∞(0,T;L2) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.",

keywords = "CH-MHD system, Crank{\textendash}Nicolson method, Error estimates, Finite element approximation, Unconditional energy stability, Unique solvability",

author = "Cheng Wang and Jilu Wang and Wise, \{Steven M.\} and Zeyu Xia and Liwei Xu",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2024",

month = jan,

day = "15",

doi = "10.1016/j.cam.2023.115409",

language = "英语",

volume = "436",

journal = "Journal of Computational and Applied Mathematics",

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TY - JOUR

T1 - Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations

AU - Wang, Cheng

AU - Wang, Jilu

AU - Wise, Steven M.

AU - Xia, Zeyu

AU - Xu, Liwei

PY - 2024/1/15

Y1 - 2024/1/15

N2 - In this paper we propose and analyze a temporally second-order accurate numerical scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations. The scheme is based on a modified Crank–Nicolson-type approximation for the time discretization and a mixed finite element method for the spatial discretization. The modified Crank–Nicolson approximation enables us to carry out the mass conservation and the energy stability analysis. Error estimates are derived for the phase field in the Lτ∞(0,T;H1) norm, and for the velocity and the magnetic fields in the Lτ∞(0,T;L2) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.

AB - In this paper we propose and analyze a temporally second-order accurate numerical scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations. The scheme is based on a modified Crank–Nicolson-type approximation for the time discretization and a mixed finite element method for the spatial discretization. The modified Crank–Nicolson approximation enables us to carry out the mass conservation and the energy stability analysis. Error estimates are derived for the phase field in the Lτ∞(0,T;H1) norm, and for the velocity and the magnetic fields in the Lτ∞(0,T;L2) norm, respectively. Numerical examples are presented to validate the theoretical results of the proposed scheme.

KW - CH-MHD system

KW - Crank–Nicolson method

KW - Error estimates

KW - Finite element approximation

KW - Unconditional energy stability

KW - Unique solvability

UR - https://www.scopus.com/pages/publications/85164224235

U2 - 10.1016/j.cam.2023.115409

DO - 10.1016/j.cam.2023.115409

M3 - 文章

AN - SCOPUS:85164224235

SN - 0377-0427

VL - 436

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 115409

ER -

Convergence analysis of a temporally second-order accurate finite element scheme for the Cahn–Hilliard-Magnetohydrodynamics system of equations

Abstract

Keywords

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