Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems

In this paper we present two types of local error estimators for the primal 8nite-element-method (FEM) by duality arguments. They are 8rst derived from the (explicit) residual error estimation method (REM) and then—as a new contribution—from the (implicit) posterior equilibrium method (PEM) using improved boundary tractions, gained by local post-processing with local Neumann problems, with applications in elastic problems. For the displacements a local error estimator with an upper bound is derived and also a local estimator for stresses. Furthermore—for better numerical e>ciency—the residua are projected energy-invariant onto reference elements, where the local Neumann problems have to be solved. Comparative examples between REM- and PEM-type local estimators show superior e@ectivity indices for the latter one.