Adaptive Virtual Element Method for Convection Dominated Diffusion Equations (Journal of Computational Mathematics, 2024)
In this paper, a robust residual-based a posteriori estimate is discussed for the Streamline Upwind/Petrov Galerkin (SUPG) virtual element method (VEM) discretization ofconvection dominated diffusion equation. A global upper bound and a local lower boundfor the a posteriori error estimates are derived in the natural SUPG norm, where the globalupper estimate relies on some hypotheses about the interpolation errors and SUPG virtualelement 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 polygonalmeshes. Numerical experiments show the robustness of the a posteriori error estimates.