A LOW ORDER NONCONFORMING MIXED FINITE ELEMENT METHOD FOR NON-STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS SYSTEM

被引：1
作者：
Yu, Zhiyun [1 ]
Shi, Dongyang [2 ]
Zhu, Huiqing [3 ]
机构：
[1] Zhongyuan Univ Technol, Coll Sci, Zhengzhou 450007, Peoples R China
[2] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China
[3] Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USA
来源：
JOURNAL OF COMPUTATIONAL MATHEMATICS | 2023年 / 41卷 / 04期
关键词：
Non-stationary incompressible MHD problem; Nonconforming mixed FEM; Optimal order error estimates; DISCONTINUOUS-GALERKIN METHODS; 2-DIMENSIONAL CURL-CURL; STATIONARY STOKES; MHD; APPROXIMATION; EQUATIONS; CONVERGENT; DISCRETIZATION; SCHEME;
D O I：
10.4208/jcm.2107-m2021-0114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by H-1(omega)-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of L-2(H-1)-norm for the velocity field, L-2(L-2)-norm for the pressure and the broken L-2(H-1)-norm for the magnetic field are derived.
引用
收藏
页码：569 / 587
页数：17
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