## 6 Discussion
It can be concluded that the displacement-based recovery technique gives more accurate stress than the stress-based recovery technique specially for boundary node where a smaller number of points are available, and displacement-based recovery technique has higher effectivity than the stress-based recovery technique. The rates of error convergence using stress and displacement recovery technique at different fineness levels for displacements, strains, and stresses errors are plotted in Figure 3. It can be observed from Figure 3 that displacement-based recovery technique results higher convergence at different fineness levels as compared to stress-based recovery technique, especially for the error recovery of state variable derivatives. The convergence rate of error with increased fineness levels for regular linear triangular elements, in original finite element solution of compressible elastic plate example for displacements, strains, and stresses, and recovered solution for displacements, strains, and stresses using displacement recovery method are found respectively as (1.9394, 2.1539), (0.9799, 1.8898), and (0.9765, 1.9012). The error convergence rate for regular quadratic triangular elements, in finite element solution for displacements, strains, and stresses, and recovered solution for displacements, strains, and stresses using displacement recovery are found respectively as (3.0473, 3.7215), (1.9869, 2.9010), and (1.9714, 2.8999). The error convergence rates are obtained in finite element results using stress recovery method for stresses as (0.9765, 1.3710) and (1.9714, 2.5018) respectively for linear and quadratic triangular elements. The higher error convergence rate is observed by employing displacement-based recovery technique for compressible and incompressible elastic problems in comparison to stress- based recovery technique. The error convergence rates are obtained in finite element results of incompressible elastic plate example using displacement and stress recovery method as (0.9818, 1.7805, and 1.4952) for stresses with quadratic triangular elements' discretization. It can be seen from the analysis results that the compressible elastic problems exhibit lower convergence rate of error as compared to incompressible elastic problems for both displacement and stress-based recovery approaches. The required adaptive meshing for predefined precision are presented in tables and figures. Tables 6, 7, 9 and 11 show global errors (FEM and post-processed), the number of elements and DOF in adaptive meshing, obtained with the linear and quadratic elements of the initial mesh respectively for elastic square plate, elastic plate with circular inclusion, and incompressible elastic square plate. The application of the displacement and stress-fitting technique-based error estimation (L\({}_{2}\)-norm-based error estimator), for guiding the improvement of meshing scheme to obtain the predefined precision in finite element analysis, is also demonstrated. Results of the adaptive refinement, for aimed error limits of displacement and gradients, are obtained for displacement and stress-fitting techniques. The aimed error of 3% is set for adaptive finite element analyses employing linear element discretization and a target error of 1% is fixed for adaptive analyses employing quadratic elements. The initial meshes are adaptively improved to bring the gradient error within the predefined precision and to distribute the error equally among all the elements. The adaptively improved meshes also indicate the distribution pattern of the errors in the problem domain. From the adaptive mesh plots, it is clear that the errors are more on corners and edges as compared to the interior of the compressible and incompressible elastic plate domain. It is concluded that the adaptive finite element analysis may predict the gradients' high error zones and can be used to improve the reliability and effectivity of solutions to the problem.