Error estimation with postprocessed finite element solutions

Fundaments of Recovery-Based Error Estimation and Bounding

“…For further information see [21][22][23] and the references therein. Once K has been obtained, the singular field (u * sing , σ * sing ) will be evaluated as in (30). u h smo is defined as the result of subtracting the singular part u * sing from the FE solution…”

“…However, in order to use it as the output of our FE code we need a method to assess the quality of this magnitude, i.e., we need to obtain an error estimate for the enhanced solution. Some authors [30] evaluate the error of the plain SPR recovered field by comparing it with some enhancements of the SPR solution, such as adding equilibrium and information of the elasticity problem. Other authors [31] also use a recovered (recycled) solution from the recovered solution.…”

Recovery based error estimation and adaptivity applied to a modified element-free Galerkin method

“…However, most of these works were applied in the context of the FEM. In this context, a relevant review on error estimators can be found in [1,6,23,25,26,27]. The most relevant classes of error estimators are the residue-based and the recovery-based error estimators.…”

Cartesian grid FEM (cgFEM): High performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization

“…al [102,103,104] also proposed to recover the displacement field, adding some equilibrium information to directly obtain a continuous recovered stress field. Wiberg and Abdulwahab [111] proposed also to obtain a recovered pair but with two different recovery procedures, one for stresses and another for the displacements. However the references related with displacement recovery procedures are not as common as those related with stress-based recovery methods.…”

“…However, in order to use it as the output of our FE code we need a method to assess the quality of this magnitude, i. e., we need to obtain an error estimate for the enhanced solution. Some authors [111] evaluate the error of the plain SPR recovered field by comparing it with some enhancements of the SPR solution, such as adding equilibrium and information of the elasticity problem. Other authors [126] also use a recovered (recycled) solution from the recovered solution.…”