@article{Jo2023, 
author = {Gwanghyun Jo and Do Y. Kwak},
title = {Immersed finite element methods for convection diffusion equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8034-8059},
keywords = {immersed finite element method, convection-diffusion problem, interface problem, control volume, upwinding scheme},
url = {https://www.sciopen.com/article/10.3934/math.2023407},
doi = {10.3934/math.2023407},
abstract = {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.}
}