h-Adaptive FE methods applied to single- and multiphase problems

A major problem in using the nite element method for solving numerous engineering problems in the framework of single- and multiphase materials is the assessment of discretization errors and the design of suitable meshes. To overcome this problem, adaptive nite element methods have been developed. Based on the error indicator by Zienkiewicz and Zhu, it is the goal of the present paper to present a new error indicator which is especially designed for multiphase problems. Furthermore, e cient h-adaptive strategies concerning both the generation of new meshes in the framework of independent and hierarchical remeshing strategies and the data transfer between old and new meshes are pointed out. Finally, numerical examples are given to exhibit the e ciency and the quality of the presented h-adaptive methods and to compare the di erent strategies to each other