Adaptive refinement in the meshless finite volume method for elasticity problems

In this paper, two adaptive refinement techniques are presented for enhancing the capability of the new kind of finite volume method called meshless finite volume (MFV) method in which the moving least squares (MLS) approximation technique is employed. The proposed algorithms perform by inserting new nodes in large error regions identified using the Zienkiewicz–Zhu (Z–Z) error estimator and the T-Belytschko (TB) stress recovery scheme. In the first method referred as CV-based adaptive refinement, the new nodes are inserted at the vertices of control volumes with higher errors. The second method, referred as GA-based adaptive refinement, contains two schemes where an adaptive refinement procedure is proposed by applying a genetic algorithm (GA) based optimization technique. To make the adaptive refinement procedure work effectively, the optimal locations of the new required nodes and the values of those effective parameters involved in the adaptive refinement are found by using GA through minimization of the global error indicator. The effectiveness and versatility of the proposed methods are demonstrated by studying three benchmark problems. It is revealed that the suggested methods achieve a predefined level of accuracy by inserting new nodes at identified locations.