Premium
Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems
Author(s) -
Ohnimus S.,
Stein E.,
Walhorn E.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.228
Subject(s) - estimator , finite element method , mathematics , neumann boundary condition , von neumann architecture , elasticity (physics) , residual , linear elasticity , duality (order theory) , mathematical optimization , mathematical analysis , boundary value problem , algorithm , physics , statistics , pure mathematics , thermodynamics , discrete mathematics
In this paper we present two types of local error estimators for the primal finite‐element‐method (FEM) by duality arguments. They are first 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 efficiency—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 effectivity indices for the latter one. Copyright © 2001 John Wiley & Sons, Ltd.