## 1 Introduction
[PERSON] and [PERSON] [17] comprehensively reviewed the error estimation approaches for linear and non-linear finite element solutions. [PERSON] and [PERSON] [18] presented the adaptive modeling of crack development for linear elastic materials under fatigue conditions. The displacement projection technique was used to calculate stress-intensity factors at each crack increment. A hybrid Hermite approximation approach and an improved interpolation element-free Galerkin method is proposed by [PERSON] et al. [19] for the analysis of elasticity problems, who found results with excellent accuracy and stability. [PERSON] et al. [20] conducted [PERSON] and [PERSON] error estimator-based adaptive analysis of magnetized plasma in transport-confined fusion reactors. The derivatives of field variable at the super-convergent points are used by [PERSON] et al. [21] to map stress field and to recover the errors in the finite element analysis by applying the artificial neural network procedure. [PERSON] et al. [22] conducted probabilistic error analysis for recently proposed statistical finite element method (statFEM) based on a Gaussian process. [PERSON] [23] compared the recently proposed influence-zones-based error-recovery techniques including RPI method for elastic finite element solutions. [PERSON] et al. [24] developed an interface model of soil and structure employing the radial point interpolation approach in finite element method. A hybrid approach using element-free Galerkin (EFG) and radial point interpolation (RPI) technique was developed by [PERSON] et al. [25] to deal with the imposition of displacement boundary conditions of the elastic problems. It is clear from the survey of the relevant literature that the recent research interest in FEM is to reduce the dependency of the mesh for the analysis, and also to increase the effectivity of the finite element solution errors. Thus, error-recovery techniques in a mesh-free environment need to be further developed particularly for adaptive finite element analysis of large deformation or incompressibility problems. The present study proposesthe mesh-free RPI-based error recovery for finite element analysis of incompressible-elastic problems. The displacement-pressure-based mixed approach is employed in finite element formulation. The elastic plate examples with a known analytical solution are analyzed to investigate the performance of RPI-based error recovery in terms of the error properties, i.e., convergence rate, distribution and effectivity. The four-node quadrilateral meshing is used for domain discretization. The effect of influence-zone type, namely circular and rectangular zones of influence, and RBF types, namely MQ and TSP radial basis function, along with their shape parameters, is also investigated in RPI-based error-recovery analysis. The RPI-based error-recovery technique performance is compared with least-square (LS)-based error-recovery technique on the conventional patches. The conventional patch contains the union of the surrounding elements around the particular element [26]. The incompressible-elastic finite element formulation and finite element error estimation procedure are given in Appendix A.