Discontinuous Galerkin methods for magnetic advection-diffusion problems

被引：1
|
作者：
Wang, Jindong [1 ]
Wu, Shuonan [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2024年 / 174卷
基金：
中国国家自然科学基金;
关键词：
Discontinuous Galerkin; Magnetic advection-diffusion; Degenerate Friedrichs system; Upwind scheme; Inf-sup condition; FINITE-ELEMENT-METHOD; RESIDUAL-FREE BUBBLES; STABILIZED GALERKIN; UNIFIED ANALYSIS; TRANSPORT; APPROXIMATIONS; CONVERGENCE; SCHEME; FLOWS;
D O I：
10.1016/j.camwa.2024.08.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We devise and analyze a class of the primal discontinuous Galerkin methods for magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we explore some terms related to convection under the vector case that provides more flexibility in constructing the schemes. Under a degenerate Friedrichs system, we show the stability and optimal error estimate, which boil down to two ingredients - the weight function and the special projection - that contain information of advection. Numerical experiments are provided to verify the theoretical results.
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页码：43 / 54
页数：12
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