Improvement of Finite Element Solutions by Postprocessing.

The first part of this research presents a method for obtaining a more accurate solution of C^0 vibration problems in finite element analysis by postprocessing. For each frequency, the method uses the computed eigenvector and the equation of motion to calculate gradients of dependent variables at element centers. Gradients at element centers are then used as sampling points in a patch recovery technique to obtain gradients at nodes. Nodal gradients are used to interpolate the dependent variables over each element. This interpolation yields the strain and kinetic energies of each element, and hence a Rayleigh quotient that provides an accurate eigenvalue. One-, two -, and three-dimensional vibration problems are used as numerical examples. The second part of this research presents a method for recovering nodal stresses of plane elasticity problems in finite element analysis. The stresses at Gauss points are determined by a standard finite element analysis. The stresses at the Gauss points are then used as sampling points in a patch recovery technique to obtained nodal stresses by determining interpolation polynomials, based on the stresses at those sampling points and coupled with the compatibility and equilibrium equations. Then nodal stress along the boundary, usually higher stress, are recovered by applying a least-squares boundary element method and satisfactory results are obtained.