Anisotropic mesh adaptation driven by a recovery-based error estimator for shallow water flow modeling

The aim of this paper is to propose an effective anisotropic mesh adaptation procedure for the solution of the shallow water equations. The hyperbolic partial differential equation system is solved via the streamline diffusion FEM, suitably modified by a shock-capturing correction. The proposed adaptation procedure relies on a recovery-based error estimator. In particular, we look for an anisotropic error estimator able to select not only the size but also the shape and the orientation of the mesh elements, with the aim of optimizing the computational advantages yielded by a standard isotropic mesh adaptation strategy. The robustness of the proposed estimator is assessed when either a single physical quantity, meaningful for the problem at hand, or a combination of all the shallow water system components drives the adaptation procedure. For this purpose, steady shallow water problems as well as unsteady configurations are considered.