A General Framework for Error Estimation in Preserving-Shapes Grid Generation in a Fluid-Dynamics Environment and Related Open Problems

A compromise for \u201ccoarse\u201d and \u201cfine\u201d mesh generation in fluid-dynamic problems is to generate adaptive and anisotropic meshes. Once an approximate solution has been achieved on a given mesh, a-posteriori error estimators and indicators can be evaluated. These are used to localize the part of the domain where is necessary further refinements or un-refinements and new element size can be determined. In this paper the comparison among several mesh generators is made to show the advantages of different choices considering also critical points in order to obtain an improvement of the discretization rule. Moreover, we present the quality of the mesh generator developed in [3] in time-dependent problems following the approach proposed in [6]