Techniques for Mesh Independent Displacement Recovery in Elastic Finite Element Solutions

In this study, techniques for mesh dependent and independent displacement recovery for an a posteriori error estimation are presented. The error recovery of the field variable is made by fitting a higher order polynomial to the displacement over a mesh independent patch (support domain) using the moving least square (MLS) interpolation procedure. The mesh dependent recovery procedure is based on the recovery of the displacement over an element patch that consists of all elements surrounding the element under consideration using the least square (LS) interpolation procedure. The two-dimensional benchmark examples are analysed using linear and quadratic triangular elements to demonstrate the effectiveness and reliability of error estimations. Global and elemental errors of a finite element solution in the energy and L2 norms are calculated directly from the post-processed displacement. The quality of error estimation obtained using the mesh independent displacement recovery technique in terms of convergence properties, effectivity and adaptive meshes under different error norms has been compared with that of the mesh dependent displacement recovery using the MLS interpolation and least square (LS) interpolation procedures. The performance of an adaptive scheme based on a mesh independent error estimator is compared with the adaptive scheme based on a mesh dependent error estimator. The numerical results show that the finite element analysis based on mesh independent recovery is very effective in converging to a predefined accuracy in a solution with a significantly smaller number of degrees of freedom