Nodal perturbations for adaptive finite element mesh generation

Abstract

A quick and easy scheme of error estimation for adaptive mesh generation is presented to construct an expert mesh generator. In finite element analysis, we solve for a solution everywhere in the domain as given by the trial function. This fact is used to estimate the perturbations in the vector potential solution at a finite element node as we go from one iteration on the mesh to the next. Every edge on which the potentials at the two vertices making up the edge, change by more than a preassigned permissible percentage is refined for the next adaptive iteration on the mesh. This approach results in convergence of the adaptive iterations and is demonstrated to give promising results.