Robust a-posteriori error estimates for weak Galerkin method for the convection-diffusion problem

We present a robust posteriori error estimator for weak Galerkin finite element method applied to stationary convection-diffusion equations in the convection-dominated regime. The provides global upper and lower bounds of is sense that are uniformly bounded with respect diffusion coefficient. we use was developed by Lin, Ye, Zhang, Zhu (2018) problem without assuming any additional conditions on convection coefficient and, has simple formulation. motivation our work comes from fact while this performs very well strongly regime, it continues exhibit poor behavior intermediate In proposed show relying adaptively refined meshes based residual-type estimator, can retrieve optimal order convergence all regimes not just Results numerical experiments presented illustrate performance estimator.