Adaptive flux-based nodeless variable finite element formulation with error estimation for thermal-structural analysis

Abstract

A posteriori error estimation for the nodeless variable finite element method is presented. A nodeless variable finite element method using flux-based formulation is developed and combined with an adaptive meshing technique to analyze two-dimensional thermal-structural problems. The continuous flux and stresses are determined by using the flux-based formulation while the standard linear element interpolation functions are used to determine the discontinuous flux and stresses. To measure the global error, the L2 norm error is selected to find the root-mean-square error over the entire domain. The finite element formulation and its detailed finite element matrices are presented. Accuracy of the estimated error is measured by the percentage relative error. An adaptive meshing technique, that can generate meshes corresponding to solution behaviors automatically, is implemented to further improve the solution accuracy. Several examples are presented to evaluate the performance and accuracy of the combined method.