Stress-based convergence analysis for p-adaptive hierarchical finite element analysis

Abstract

An important step in any finite element analysis is to determine the accuracy of the model used. For linear elastic analyses, accuracy can be measured by the convergence of the solution. Typically error norms based on the strain energy of the system are employed. However, this method of error calculation is ineffective in regions of large stress gradients or concentrated loads. This paper studies the effectiveness of including an a posteriori L 2 error norm to measure the convergence of the stress solution of a hierarchic p-adaptive program. This norm is compared to a strain energy based a priori error measure for two example cases. It is determined that the L 2 stress error norm effectively measures elemental convergence particularly in regions of large stress gradients, and it can be used effectively with the a priori error estimator to determine when a solution has converged within a given tolerance.