AIMS Mathematics | |
Immersed finite element methods for convection diffusion equations | |
article | |
Gwanghyun Jo1  Do Y. Kwak2  | |
[1] Department of Mathematics, Kunsan National University;Department of Mathematical Sciences | |
关键词: immersed finite element method; convection-diffusion problem; interface problem; control volume; upwinding scheme; | |
DOI : 10.3934/math.2023407 | |
学科分类:地球科学(综合) | |
来源: AIMS Press | |
【 摘 要 】
In this work, we develop two IFEMs for convection-diffusion equations with interfaces. We first define bilinear forms by adding judiciously defined convection-related line integrals. By establishing Gårding's inequality, we prove the optimal error estimates both in $ L^2 $ and $ H^1 $-norms. The second method is devoted to the convection-dominated case, where test functions are piecewise constant functions on vertex-associated control volumes. We accompany the so-called upwinding concepts to make the control-volume based IFEM robust to the magnitude of convection terms. The $ H^1 $ optimal error estimate is proven for control-volume based IFEM. We document numerical experiments which confirm the analysis.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202302200002771ZK.pdf | 712KB | download |