## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Recovery Type**} & \multicolumn{2}{c}{**Adaptive Analysis Results (Original Uniform Mesh with 233 Elements and 534 DOE, 2% Target Error)**} \\ \cline{2-5}  & **FEM Error** & **Projected Error** & **Adaptive Mesh Properties** \\ \hline LS (conventional patch) & 4.93 & 5.12 & 739 & 1586 \\ RPI (Meshfree-MQ-Clr.) & 4.93 & 9.35 & 291 & 652 \\ RPI (conventional patch-MQ) & 4.93 & 4.02 & 346 & 770 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Adaptive finite element analysis results (errors, total number of elements (N) and DOF) for incompressible-elastic plate with 2% target error using quadrilateral elements. -based RPI-recovery approach have higher global effectivity than the conventional patch-based LS error-recovery approach, with more optimize error distribution characteristics. The effect of influence-zone type, namely circular and rectangular zones of influence, and RBF type, namely MQ and TSP radial basis function, is also investigated in RPI-based error-recovery analysis. The results indicated that influence-zone and RBF type affect considerably the error quality and effectivity in RPI-based error-recovery analysis. The rectangular zone of influence improves the error convergence and reduces the order of error, while performance of TSP radial basis function is better than the MQ radial basis function in RPI-based error recovery in incompressible-elastic problem. The error convergences' infinite element solutions using circular and rectangular influence-zone-based RPI recovery with TSP RBF are 1.93875 and 2.12271. The optimal value of the shape parameter (\(\eta\)) of TSP radial basis function is four (4), as by increasing the \(\eta\) value, the order of error increases and rate of error convergence decreases. The error distribution pattern is replicated in adaptively improved meshes that resulted from adaptive analysis to obtain a target error limit throughout the problem domains. The adaptive analysis incorporating the error recovery based on RPI is carried out for target error limits of 4% and 2%, respectively, for square plate and plate with rigid circular opening. The degrees of freedom and total number of elements (N) after mesh updated for target error with RPI-recovery techniques using quadrilateral discretization are presented in Tables 6 and 8. The updated mesh plots for the target error obtained in RPI-recovery techniques considering influence zones/standard patches and MQ/TSP radial basis function are shown in Figures 4 and 6. It is observed from the updated meshes that the RPI error computation is more efficient as compared to the standard patch-based error computation. It can be concluded that the adaptive analysis using radial-point interpolation-based error-recovery estimation provides results with excellent accuracy and reliability. that for the least-square error-recovery technique. The performance of RPI influence-zone-based recovery is better as compared to conventional patches-based RPI error recovery. It is observed that influence-zone and RBF type affect considerably the error quality and effectivity in RPI-based error-recovery analysis. The rectangular zone of influence improves the error convergence and reduces the order of error, while performance of TSP radial basis function is better than the MQ radial basis function in RPI-based error recovery in the incompressible-elastic problem. It can be concluded that the adaptive analysis under the guidance of radial point interpolation-based error-recovery estimation provides results with excellent accuracy and reliability. Conceptualization, M.A. ; methodology, N.B.K. ; validation, N.B.K. and S.A.; formal analysis, M.A. and S.A.; investigation, N.B.K. ; resources, N.B.K. ; writing--original draft preparation, M.A. ; writing--review and editing, N.B.K. visualization, S.A.; supervision S.A.; project administration, S.A.; funding acquisition, M.A. All authors have read and agreed to the published version of the manuscript.