Maximum norm<i>a posteriori</i>error estimates for convection–diffusion problems

Abstract We prove residual-type a posteriori error estimates in the maximum norm for linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar analysis energy by Verfürth indicates dual of convective derivative must added to natural order residual estimator reliable and efficient. show situation is similar norm. In particular, we define mesh-dependent weighted seminorm error, which functions as maximum-norm counterpart used setting. The total then defined sum this seminorm, data oscillation. shown equivalent notion, with constant independent singular perturbation parameters. These are proved under assumption certain hold Green’s function at hand. Numerical experiments confirm our estimators effectively capture behavior perturbed problems, can drive adaptive refinement layer phenomena.