Structured mesh adaption: space accuracy and interpolation methods

Abstract In this paper, we review the main stages of the construction of a variational method to optimize and to adapt two- and three-dimensional structured grids. The formalism and the notation presented enable a constructive and comprehensive description of the adaption process. The major part of this paper is devoted to the study of various interpolation methods which are used for the correct space localization of the adaption, for cell center/cell vertex recovery and for overlapping grids interpolation. In particular, the behavior of the linear interpolation, least square minimization and Taylor series expansion methods are investigated. Several examples of the methods described and the combination of adaption and interpolation are presented showing their possibilities.