Adaptive Virtual Element Method for Convection Dominated Diffusion Equations

In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization of convection dominated diffusion equation.A global upper bound and a local lower bound for the a posteriori error estimates are derived in the natural SUPG norm, where the global upper estimate relies on some hypotheses about the interpolation errors and SUPG virtual element discretization errors.Based on the Dörfler's marking strategy, adaptive VEM algorithm drived by the error estimators is used to solve the problem on general polygonal meshes.Numerical experiments show the robustness of the a posteriori error estimates.