Robust globally divergence-free HDG finite element method for steady thermally coupled incompressible MHD flow

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-08-29 DOI:10.1016/j.apnum.2025.08.007

Min Zhang , Zimo Zhu , Qijia Zhai , Xiaoping Xie

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引用次数: 0

Abstract

This paper develops a hybridizable discontinuous Galerkin (HDG) finite element method of arbitrary order for the steady thermally coupled incompressible Magnetohydrodynamics (MHD) flow. The HDG scheme uses piecewise polynomials of degrees

k (k \geq 1), k, k - 1, k - 1

and

k

respectively for the approximations of the velocity, the magnetic field, the pressure, the magnetic pseudo-pressure, and the temperature in the interior of elements, and uses piecewise polynomials of degree

k

for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. Existence and uniqueness results for the discrete scheme are given and

O (h^{k})

- optimal error estimates are derived for all the variables. Numerical experiments are provided to verify the obtained theoretical results.

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稳定热耦合不可压缩MHD流动的鲁棒全局无散度HDG有限元方法

本文针对稳态热耦合不可压缩磁流体动力学（MHD）流动问题，提出了一种任意阶的杂化不连续Galerkin （HDG）有限元方法。HDG格式分别采用k（k≥1）、k、k−1、k−1、k−1和k次分段多项式来逼近元件内部的速度、磁场、压力、磁伪压力和温度，并采用k次分段多项式来逼近元件界面上的数值迹线。该方法可以得到速度和磁场的全局无发散近似。给出了离散格式的存在唯一性结果，并得到了所有变量的0 (hk)-最优误差估计。数值实验验证了所得理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.