Adaptive mesh generation preserving the quality of the initial grid

An algorithm allowing the automatic generation of a mesh and accounting for the main physical features of the problem is presented. The adaptivity is provided by a refinement strategy which preserves the characteristics of the initial grid, inserting nodes only in the regions where the solution deviates from a linear behavior. A geometrical interpretation in terms of a monitor surface is given, and various different approaches to the problem are discussed. The efficiency of the algorithm is enhanced by a local solution scheme, which uses previously computed values of all the unknown quantities as boundary conditions for the newly generated nodes. A few examples illustrate the performance of the algorithm