Adaptive Nearest-Nodes Finite Element Method and Its Applications

Abstract

In this paper, an adaptive finite element method is formulated based on the newly developed nearest-nodes finite element method (NN-FEM). In the adaptive NN-FEM, mesh modification is guided by the gradient of strain energy density, i.e., a larger gradient requires a denser mesh and vice versa. Mesh intensity is introduced to correlate gradient of strain energy density and mesh density. Relative error in the total potential energy is used to indicate when mesh modification should be stopped. Numerical examples are presented to demonstrate the performance of the proposed adaptive NN-FEM.