Abstract: Optimization of finite element grids based on the minimum potential energy is important both in theory and practice. By means of this method, the most accurate numerical results can be obtained with the least degrees of freedom. In this paper, two kinds of procedures are presented as typical adaptive processes in grid optimization.A series of examples including some research work by Dr. JVC. Zhu, Dr. Y.C.Liu and the author under the guidance of Prof. Zienkiewicz: are given to show the validity and versatili...