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An error indicator for parameter identification with stabilized mixed tetrahedrals

The identification of parameters in constitutive laws considering inhomogeneous states of stress and strain is realized by iteratively minimizing a least squares functional. In each iterative step of this optimization problem a finite element analysis is carried out which results in a significant higher numerical cost than a single finite element analysis. Consequently, an efficient discretization is required to keep the numerical cost low. To address this problem an adaptive mesh refinement is considered which is based on a posteriori error indicators [1] leading to refinements appropriate to the parameter identification problem. The goal is to apply the error indicators to the finite element method for tetrahedral elements of low order which are preferable for adaptive mesh refinements and in addition reduce computational effort. Additional stabilization terms in the element formulation [4, 6] reduce volume locking effects making the elements suitable for (nearly) incompressible material behavior. Numerical examples illustrate the progress on this work. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)