Scalable recovery-based adaptation on Cartesian quadtree meshes for advection-diffusion-reaction problems

We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems. The adapta- tion process is driven by a recovery-based a posteriori estimator for the L2(Ω)- norm of the discretization error, based on suitable higher order approximations of both the solution and the associated gradient. In particular, a metric-based approach exploits the information provided by the estimator to iteratively pre- dict the new adapted mesh. The new mesh adaptation algorithm is successfully assessed on different configurations and performs well when dealing with dis- continuities in the data as well as in the presence of internal layers not aligned with the Cartesian directions. A cross-comparison with a standard estimate- mark-refine approach and with other adaptive strategies available in the liter- ature shows the noteworthy accuracy and parallel scalability of the proposed approach.