Adaptive nearest-nodes finite element method guided by gradient of linear strain energy density

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. A finite element mesh is iteratively modified by a set of operators, including mesh refinement, mesh coarsening and mesh smoothing, to make its density conform the gradient of strain energy density. The selection of a proper operator for a specific mesh region is determined by a set of criteria based on mesh intensity. The iteration loop of mesh modification is stopped when the relative error in the total potential energy is less than a prescribed accuracy. Numerical examples are presented to demonstrate the performance of the proposed adaptive NN-FEM.