ON THE CHARACTERIZATION OF FINITE-DIFFERENCES OPTIMAL MESHES

Regridding methods has become an important tool in the integration of PDE systems whose solutions exhibit sharp transitions in spatial derivatives. This paper improves the results presented in an earlier contribution of the author and F. Oliveira (1988). Theoretical justifications of finite differences regridding criteria for the transport and heat equations are presented. The nonuniform meshes in the physical space are generated by the use of coordinate transforms which map them into uniform meshes in the computational space. After the two mesh systems have been generated two approaches are used for solving the PDE: to construct the approximations on the uniform mesh in the computational space or to construct the finite-difference approximations on the nonuniform mesh in the physical space. In this paper we are concerned with the question of the relationship between the two approaches, namely the characterization of the mesh density (coordinate transform) which improves the spatial accuracy of the approximation in the physical (computational) space.