immersed finite element method; convection-diffusion problem; interface problem; control volume; upwinding scheme; Mathematics; QA1-939
Issue Date
2023-01
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Citation
AIMS MATHEMATICS
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 and -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 optimal error estimate is proven for control-volume based IFEM. We document numerical experiments which confirm the analysis.