Alternative mesh optimality criteria for h-adaptive finite element method
Adaptive strategies are a necessary tool to make finite element analysis applicable to engineering practice. In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to attain a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In this paper we propose the use of alternative mesh optimality criteria with an h-adaptive procedure for 2D elastic problems. The alternative mesh optimality criteria allow us to attain maximum of accuracy with a prescribed number of elements or a prescribed memory size or a prescribed cpu time. These adaptive strategies are based on a technique of error in constitutive relation and adapted techniques of construction of admissible fields (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes account the steep gradient areas. Some examples show the efficiency of the method.
mesh adaptivity discretization errors h-adaptivity remeshing adaptive optimality criteria