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 adaptation 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 predict the new adapted mesh. The new mesh adaptation algorithm is successfully assessed on different configurations and performs well when dealing with discontinuities in the data as well as in the presence of internal layers not aligned with the Cartesian directions. A cross-comparison with a standard estimatemark-refine approach and with other adaptive strategies available in the literature shows the noteworthy accuracy and parallel scalability of the proposed approach.