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

• 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.

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.