Immersed finite element methods for convection diffusion equations

AIMS Mathematics

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