Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems. (English) Zbl 0954.74072

Summary: First, we give a survey of existing residuum-based error estimators and error indicators. Generally, residual error estimators (which have at least upper bound in contrast to indicators) can be locally computed from residua of equilibrium and stress-jumps at element interfaces using Dirichlet or Neumann conditions for element patches or individual elements (REM). Another equivalent method for error estimation can be derived from a posteriori computed improved boundary tractions which provide exact equilibrium of elements. They are computed from local Neumann problems and yield improved local solution by testing with higher test functions. This method is called posterior equilibrium method and yields better efficiency indices than REM for the investigated problem, even in case of locking. Also, the important feature of model adaptivity via hierarchical error estimation can only be realized by this strategy. Global Neumann-type estimators and examples are presented for elastic and elastoplastic deformations, controlling equilibrium in tangential space.


74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
74B05 Classical linear elasticity
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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