Testing the quality of grids generated using the direct approach

In testing the quality of grids, several measures have been introduced; however, as long as the main goal of grid generation is to solve partial differential equations, we have approximated the solution of some simple boundary value problems and propose to measure the grid quality by looking at the error. The grids used are obtained using the discrete approach (direct approach) of grid generation. The discretization of the partial differential equations is made using finite-difference schemes and the mapping method.