Abstract
A finite element method coupled with error estimation has gained considerable prominence in industry. However, effective and reliable error control of finite element solution is always a challenging task particularly for incompressible and large deformations problems. Effective interpolation type gradient recovery based error estimation procedure is proposed in the present study. The recovery is based on Moving Least Squares approximation (mesh free approach) of the displacement field or their derivatives by a higher order polynomial over a patch of nodes in a circular boundary. The performance of error estimation scheme in terms of its effectivity and convergence has been compared with that of Zienkiewicz-Zhu (ZZ) super-convergent recovery scheme by applying the scheme to benchmark elastic problems. Error estimators compute the error in energy norm of the recovered solution both at local and global levels. The adaptive meshing based on guidance of the local error predicted by ZZ and proposed interpolation type error estimators, is also used to study the error distribution in the domain. The proposed mesh independent node patch based recovery scheme is found to be better than that for the mesh dependent node patch based ZZ super convergent recovery scheme.DOI: http://dx.doi.org/10.5755/j01.mech.24.5.19937
Highlights
Finite Element Method (FEM) is a powerful technique for simulating real life problems, but it is only able to provide an approximated solution that necessitates reliable error control of computed solutions
A posteriori error estimate based on an equilibrated stress reconstruction that is obtained from mixed finite element solutions of local Neumann linear elasticity problems is presented in [9]
The present study aimed to present a recovery of higher derivative of field variable utilizing moving least squares (MLS) technique over a patch of mesh independent nodes for formulating a posteriori error estimator
Summary
Finite Element Method (FEM) is a powerful technique for simulating real life problems, but it is only able to provide an approximated solution that necessitates reliable error control of computed solutions. A posteriori error estimate based on an equilibrated stress reconstruction that is obtained from mixed finite element solutions of local Neumann linear elasticity problems is presented in [9]. In [15], a moving least squares (MLS) recovery-based procedure to obtain postprocessed smoothed stresses field is presented in which the continuity of the recovered field is provided by the shape functions of the underlying mesh. The performance of proposed error estimator is compared on benchmark elastic problems with ZZ error estimator [10], which evaluates the error using the recovery technique based upon the least square fitting of stress field over a mesh dependent nodes patch, in term of effectivity and rate of convergence
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