A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection–diffusion problems

• Published in: Journal of computational and applied mathematics Vol. 313; pp. 152 - 167
• Main Authors: Liu, Li-Bin, Chen, Yanping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.03.2017
• Subjects: Adaptive algorithms; Algorithms; Convection–diffusion; Error analysis; Finite difference method; Mathematical analysis; Mathematical models; Maximum norm; Monitors; Norms; Singularly perturbed; Strongly coupled; Maximum norm; Singularly perturbed; Convection–diffusion; Strongly coupled
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2016.08.020

A system of two singularly perturbed convection–diffusion problems with strong coupling is studied. This system is discretized by an upwind finite difference scheme on an arbitrary non-uniform mesh. An a posteriori error estimation in the maximum norm is derived. Based on the a posteriori error estimation, a monitor function is proposed to design an adaptive grid algorithm. Especially, to implement the adaptive grid approach, we not only give a mesh generation algorithm, but also give a sub-algorithm, which is called an arc-length equidistribution algorithm. Numerical results are given to confirm our theoretical result. •A maximum norm a posteriori error estimation is presented.•A monitor function is proposed to design an adaptive grid algorithm.•We give a sub-algorithm, which is called an arc-length equidistribution algorithm.