Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions

Abstract

SUMMARYPatch recovery based on superconvergent derivatives and equilibrium (SPRE), an enhancement of the Superconvergent Patch Recovery (SPR), is studied for linear elasticity problems. The paper also presents a further improvement for recovery of derivatives near boundaries, SPREB, where either tractions or displacements are prescribed. This is made by inclusion of weighted residual errors at boundary points in the patch recovery. A pronounced improvement in the post processed gradients of the finite element solution is observed by this method.

Interlaminar stress recovery for three-dimensional finite elements

“…Many investigators have modified this procedure to include satisfaction of boundary conditions [24,25,26]. For a more accurate prediction of the transverse stresses in laminated composites and shells, a Modified Super-convergent Patch Recovery (MSPR) technique has been derived to obtain accurate nodal in-plane stresses which, subsequently, are used in the integration along the thickness of the equilibrium equations for evaluating the transverse shear and normal stresses [27].…”

A recovery-explicit error estimator in energy norm for linear elasticity

“…In general they couple the stress components in order to be able to add constraints that improve the quality of the recovered field. Wiberg and Abdulwahab [45,25] proposed to take into account the equilibrium of the recovered field by using a penalty method, Blacker and Belytschko [26] introduced the "Conjoint Polynomial Enhancement" to improve the recovered field along the boundaries. Other techniques looking for equilibrated recovered solutions for upper bounding purposes can be found in [46,47,48,49], but always presenting small lacks of equilibrium even at patch level, thus preventing the strict upper bound property.…”

“…The recovery-based error estimators are robust, easy to implement and are used in commercial codes. The publication of the original SPR technique was followed by several works aimed to improve its quality, see for example [25,26,27]. Ródenas et al proposed to add constraints to impose local equilibrium and local compatibility to the recovered solution in the FEM framework [28] bringing up the SPR-C technique that was also adapted to the eXtended Finite Element Method (XFEM) framework [29,30].…”

A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

“…Generally, it is well known that the main drawback of recovery type techniques is the lack of accuracy along the boundaries of the domain. Further improvements to the SPR technique have been introduced [24][25][26][27] in order to prevent the lack of accuracy of the smoothed field along the boundaries of the domain and also to increase the accuracy into the domain.…”