## 4 Discussion  
The study implements the RPI-based error-recovery approaches in finite element error analysis. The displacement/pressure-based mixed approach is used in finite element formulation. The accuracy and reliability of RPI-based error-recovery approaches is assessed for incompressibility-elastic problem. The adaptive analysis computational results are obtained for error quality, i.e., errors convergence, effectivity with increasing order of fineness and refined meshes for target error, by simulating the incompressible plate benchmark examples. The problem domain is meshed using 4/9 node quadrilateral elements. The target error in energy norm for four-node elements is kept as 4% in incompressible-elastic plate and 2% for incompressible-elastic plate with rigid circular opening. The incompressible-elastic analysis results for plate problems in terms of convergence of error, effectivity for least-square and radial point interpolation-based recovery procedures using influence zones/standard patches, and MQ/TSP radial basis function and two-shape parameter value (\(\eta\) =4, 5) are tabulated in Tables 1-9. From Tables 1-6, it is clear that the error convergence obtained with the help of the RPI recovery is found to be better than that for the least-square error-recovery technique. The performance of RPI influence-zone-based recovery is better as compared to conventional patches-based radial-point interpolation error recovery. This may be due to inaccurate recovery for nodes on boundary since fewer nodes are available. The influence-zone-based recovery technique eliminates such difficulties. The order of error is also smaller in RPI error recovery, thereby indicating higher efficiency of the RPI-based error-recovery technique. The higher order quadrilateral elements also present similar error properties results for RPI error-recovery-based adaptive finite-element analysis. However, error convergence in conventional patch-based RPI error-recovery technique is higher compared to influence-zone-based RPI error-recovery technique. The convergence of errors in the original finite element solution, and in the solution employing circular influence-zone-based RPI recovery with MQ RBF, conventional patch-based RPI recovery with MQ RBF and conventional patch-based least-square (LS) error recovery, are found as (0.97772, 2.03291, 1.97929 and 1.6740) and (1.99607, 3.53087, 4.26621 and 2.54955), respectively, for four-node and nine-node quadrilateral discretization of elastic plate problem. The performance of RPI-based error-recovery approach is also investigated for the plate problem with circular opening. It is evident from the Tables 7 and 8 and Figure 6 that computation results of influence-zone \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Mesh Size**} & \multirow{2}{*}{**FEM Error**} & \multicolumn{2}{c}{**RPI (Influence Zone, MQ)**} & \multicolumn{2}{c}{**RPI (Conventional Patch, MQ)**} & \multicolumn{2}{c}{**LS (Conventional Patch)**} \\ \cline{3-8}  & & & **Error** & **Effectivity** & **Error** & **Effectivity** & **Error** & **Effectivity** \\ \hline
233 & 534 & 0.1680 & 0.1071 & 0.88526 & 0.1148 & 0.81606 & 0.1177 & 1.03672 \\
793 & 1698 & 0.0912 & 0.0584 & 0.98995 & 0.0604 & 0.98564 & 0.0516 & 1.02639 \\
2467 & 5130 & 0.0546 & 0.0266 & 0.95198 & 0.0272 & 0.94467 & 0.0234 & 0.97784 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Error properties found for LS- and RPI (MQ)-based recovery approach in incompressible-elastic analysis for plate with rigid circular opening considering influence zones and conventional patches. (Four-node quadrilateral equal elements).