Post-Processing and A Posteriori Error Estimation of Finite Element Solutions

A new method for finite element postprocessing has been implemented for three-dimensional continuum analysis. The method provides ways to enhance the stress solution relative to conventional postprocessing methods. Recent literature demonstrated the technique for one and two dimensions. The current work extends the method to analysis in three dimensions, specifically using tetrahedral elements. This is the first known implementation of this technique for three dimensional problems. Significant improvements in stress results are found. In addition, an a posteriori error estimator has been developed based on the enhanced stress solution. Local and global error estimators are defined and these are particularly attractive when used with free meshing programs. The method has been implemented to work with commercial finite element programs (NASTRAN and PATRAN). The formulation and implementation are described. Several examples using this scheme are presented.