Mesh-Free MLS-Based Error-Recovery Technique for Finite Element Incompressible Elastic Computations

The finite element error and adaptive analysis are implemented in procedures to increase the reliability of numerical analyses. In this paper, mesh-free error-recovery technique based on moving least squares (MLS) interpolation is applied recover errors stresses displacements incompressible elastic solutions estimated energy norms. effects types (triangular quadrilateral elements) formation patches (mesh-free patch, mesh-dependent element-based node-based patch) for recovery MLS conventional least-square interpolation-error quantification also assessed study. Numerical examples elasticity, including a problem with singularity, studied display effectiveness applicability technique. mixed formulation (displacement pressure) adopted problem. rate convergence, effectivity estimation, modified meshes desired accuracy used assess estimators. error-convergence rates computed original FEM solution, post-processed solution using MLS-based displacement, stress recovery, patch-based least-square-based (ZZ) as (0.9777, 2.2501, 2.0012, 1.6710 1.5436), (0.9736, 2.0869, 1.6931, 1.8806 1.4973), respectively, four-node quadrilateral, six-node triangular meshes. It concluded that displacement-based was more effective than stress-based patches.