For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators, we propose an adaptive mesh-refining algorithm for SUPG and prove that the generated SUPG solutions converge at asymptotically optimal rates towards the exact solution.
@article{arxiv.1806.11000,
title = {Optimal Adaptivity for the SUPG Finite Element Method},
author = {Christoph Erath and Dirk Praetorius},
journal= {arXiv preprint arXiv:1806.11000},
year = {2019}
}