## 1 Introduction
[PERSON] and [PERSON] [15] have presented a global field variable derivative recovery technique in L\({}_{2}\)-norm for extended finite elements. A dual error estimator for the conforming finite element technique, developed using the explicit residual and the enhanced Zienkiewicz-Zhu (ZZ) error estimator, is presented by [PERSON] et al. [16]. [PERSON] et al. [17] have proposed an approximation technique to create a continuous field and implemented the mesh refinement procedure to obtain a uniform error distribution over the domain. [PERSON] et al. [18] proposed an error estimator based on element energy projection technique for adaptive finite element analysis. [PERSON] et al. [19] have presented a procedure to recover the stress solution error for low-order 3D finite elements and the recovered stress field satisfies the equilibrium in an average sense. The mesh free recovery technique using the element free Galerkin (EFG) method has also been developed to recover the finite element solution error. A mesh free error recovery technique to recover the displacement field of elastic finite element analysis is proposed by [PERSON] [20]. The performance of mesh free MLS interpolation-based a posteriori error recovery technique is investigated by [PERSON] et al. [21] considering different discretization scheme, recovery points, and recovered derivative of field variables. They found that effectivity of proposed mesh free a posteriori error technique for stress extraction is comparable to ZZ error technique. [PERSON] et al. [22] have proposed a finite element meshing scheme for the incompressible elasticity problems giving optimal convergence with mesh refinement. The scheme consists of the combination of a mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures. [PERSON] and [PERSON] [23] have extended the unfitted finite element method and have demonstrated a converged L\({}_{2}\)-error analysis of the method applied to an interface problem. To smooth out the derivative at inter-element boundaries or nodes, better approximated derivatives at nodes are required, and to calculate the derivative at any point in the element domain, a better approximate displacement field is needed. This can be achieved by least square fit of the computed Gauss point stress or displacement using the higher degree polynomial over node patches. The difference between the displacement/stress/strain from the finite element results and projected displacement/stress/strain from post-processed results provides the error in the finite element solution. Most of the existing study paid attention to the recovery of errors in stresses employing node-based patches, and errors are represented in energy norms. The present study represents the errors at local and global level in quantity of interest, i.e., displacement or gradients based on L\({}_{2}\)-norm. The study considers larger patch size, i.e., element-based patch, to recover the errors in displacement to improve the effectiveness of a posteriori error recovery technique at domain boundaries. The effectiveness of L\({}_{2}\)-norm-based error estimators are also investigated for the adaptive finite element analysis of incompressible elastic problems. Therefore, the present study is a contribution to further investigate the least squares interpolation-based a posteriori error recovery technique for recovery of stress and displacement using larger patch size, and implemented to compressible and incompressible elastic problems. The elastic benchmark examples of compressible and incompressible elastic bodies, with linear and quadratic triangular discretization schemes, are solved to quantify the finite element error in displacement or gradients. The quality of error estimation in a posteriori recovery techniques are enumerated and matched in terms of convergence properties, effectivity, and adaptively updated meshes for predefined precision.