@article{Mai2023, 
author = {Xiongfa Mai and Ciwen Zhu and Libin Liu},
title = {An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {4},
pages = {1528-1538},
keywords = {singularly perturbed, discontinuous convection coefficient, adaptive grid algorithm, a posteriori error estimate},
url = {https://www.sciopen.com/article/10.3934/nhm.2023067},
doi = {10.3934/nhm.2023067},
abstract = {In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.}
}