@article{Huang2026, 
author = {Jian Huang and Zhongdi Cen and Xianbin Wu},
title = {A novel numerical method on a posteriori mesh for a singularly perturbed convection-diffusion problem with mixed type boundary conditions},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {2},
pages = {387-401},
keywords = {singularly perturbed, convection-diffusion, difference method, a posteriori error analysis, mesh equidistribution},
url = {https://www.sciopen.com/article/10.3934/nhm.2026018},
doi = {10.3934/nhm.2026018},
abstract = {This article introduces a novel numerical method for solving a singularly-perturbed convection-diffusion problem with mixed type boundary conditions. The approach begins by transforming the second-order boundary value problem into a system of first-order differential equations. The stability result of its corresponding differential operator vector is obtained although the system of equations is in a special form. The transformed system is approximated through a hybrid difference method, followed by a posteriori error analysis that relies on the stability result of the differential operator vector. A posteriori mesh and approximation solution are derived by designing a solution-adaptive algorithm derived from the a posteriori error bound. Finally, the second-order uniform convergence of the novel numerical method is corroborated by numerical experiments.}
}