Maximum norm a posteriori error estimates for convection-diffusion problems

@article{Demlow2022MaximumNA,
  title={Maximum norm a posteriori error estimates for convection-diffusion problems},
  author={Alan Demlow and Sebastian Franz and Natalia Kopteva},
  journal={ArXiv},
  year={2022},
  volume={abs/2207.08251}
}
We prove residual-type a posteriori error estimates in the maximum norm for a linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar error analysis in the energy norm by Verfürth indicates that a dual norm of the convective derivative of the error must be added to the natural energy norm in order for the natural residual estimator to be reliable and efficient. We show that the situation is similar for the maximum norm. In particular, we define a mesh… 
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