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

被引：17
|
作者：
Dong, Xiaojing [1 ,2 ]
He, Yinnian [3 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Key Lab Intelligent Comp & Informat Proc,Minist E, Xiangtan 411105, Peoples R China
[2] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China
[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 11-12期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
MHD equations; Semi-implicit scheme; Crank-Nicolson extrapolation scheme; Stability and convergence; Finite element method; FINITE-ELEMENT APPROXIMATION; NAVIER-STOKES PROBLEM; ITERATIVE METHODS; STATIONARY; DISCRETIZATION; STABILITY; EQUATIONS;
D O I：
10.1016/j.camwa.2018.08.060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers a Crank-Nicolson extrapolation scheme based on mixed finite element method to solve the three-dimensional incompressible magnetohydrodynamics (MHD) equations. We prove that the fully discrete scheme is almost unconditionally stable and convergent, i.e., stable and convergent when the time step is less than or equal to a constant. By a new negative norm technique, the optimal error estimates in L-2-norm are derived. Meanwhile, the numerical investigations provide a sufficient support for the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2678 / 2700
页数：23
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