Moving Least Squares Interpolation Based A-Posteriori Error Technique in Finite Element Elastic Analysis

The performance of a-posteriori error methodology based on moving least squares (MLS) interpolation is explored in this paper by varying the finite element error recovery parameters, namely recovery points and field variable derivatives recovery. The MLS interpolation based recovery technique uses the weighted least squares method on top of the finite element method's field variable derivatives solution to build a continuous field variable derivatives approximation. The boundary of the node support (mesh free patch of influenced nodes within a determined distance) is taken as circular, i.e., circular support domain constructed using radial weights is considered. The field variable derivatives (stress and strains) are recovered at two kinds of points in the support domain, i.e., Gauss points (super-convergent stress locations) and nodal points. The errors are computed as the difference between the stress from the finite element results and projected stress from the post-processed energy norm at both elemental and global levels. The benchmark numerical tests using quadrilateral and triangular meshes measure the finite element errors in strain and stress fields. The numerical examples showed the support domain-based recovery technique's capabilities for effective and efficient error estimation in the finite element analysis of elastic problems. The MLS interpolation based recovery technique performs better for stress extraction at Gauss points with the quadrilateral discretization of the problem domain. It is also shown that the behavior of the MLS interpolation based a-posteriori error technique in stress extraction is comparable to classical Zienkiewicz-Zhu (ZZ) a-posteriori error technique.