## 1 Introduction  
The error assessment and adaptive techniques are developed to improve the finite element analysis efficiency and to keep the discretization error within limits. The adaptive finite element technique is an iterative approach in which the finite element analysis and error estimation are first carried out, and then the solution error is checked for permissible limits, and the mesh is refined if limit is exceeded. The success of adaptive analysis depends on the accurate error estimation of selected meshing schemes. The current interest in finite element method (FEM) research is to reduce the dependency of mesh for the analysis and to develop the advanced finite element methods. [PERSON] et al. [1] provided a review of up-to-date high-performance finite element methods including the hybrid stress-function FEM, the hybrid displacement-function FEM and the improved unsymmetric FEM, and their applications. [PERSON] and [PERSON] [2] proposed a meshfree finite element method based on partition of unity for linear and nonlinear finite element analyses. The shape-free FEM concept was proposed by [PERSON] et al. [3], in which performances of FEM are not affected by distortion of element shapes. Three-dimensional eight-node hexahedral elements are developed by [PERSON] et al. [4] for resisting mesh distortion in the finite element analysis applicable to both isotropic and anisotropic cases. They apply the virtual work principle in the development of an element considering two different sets of displacement fields that are employed simultaneously, namely traditional iso-parametric element formulations and analytical trial functions. [PERSON] et al. [5] developed a new three-dimensional solid-shell element with mesh-resistant distortion for analysis of shells with various geometry and loading conditions. The incompressible condition of problem causes an error in analysis due to the ill conditioning of the stiffness matrix and volumetric locking. [PERSON] and [PERSON] [6] summarized the computational results of the approaches, namely displacement-pressure formulation, a three-field formulation and a two-field formulation based on an energy functional that deals with the incompressibility in finite element analysis. [PERSON] and [PERSON] [7] used a mixed Kirchhoff stress displacement-pressure formulation, [PERSON] et al. [8] used a basic pressure projection stabilized method, and [PERSON] et al. [9] use a selective-reduction integration approach to satisfy the incompressibility condition. [PERSON] and [PERSON] [10] suggested a number of treatments for the issue of volumetric locking, which arises from the constrained nature of displacement-based finite element analysis. They consider hydrostatic pressure as unknown and satisfy the condition of the ellipticity on the kernel, in addition to the well-known Babuska-Brezzi condition. [PERSON] et al. [11] employed the variational multi-scale approach-based finite element technique to investigate finite-strain incompressible elasticity with volumetric locking. The meshless method provides better accuracy than conventional FEM [12]. [PERSON] et al. [13] proposed a universal recovery procedure to improve the accuracy of gradient approximation for virtual element methods using general polygonal meshes. [PERSON] and [PERSON] [14] developed the nodal stress recovery technique by fitting appropriative function using Colliding Bodies Optimization (CBO) Algorithm for nodal stress fields. The approach is a connection between analytical approaches and numerical methods, utilizing the benefits of both categories. [PERSON] et al. [15] implemented the mixed formulations for incompressible linear elasticity problems in the finite element method. They also consider the requirement for pressure stabilization with lowest-order conforming approximations. [PERSON] et al. [16] developed mathematical algorithms to generate mesh using ordered/unordered point clouds, eliminating the errors which can be induced in mesh generation over the domains.