A functional type a posteriori error analysis for the Ramberg-Osgood model

We discuss the weak form of the Ramberg-Osgood equations (also known as the Norton-Hoff model) for nonlinear elastic materials and prove functional type a posteriori error estimates for the difference of the exact stress tensor and any tensor from the admissible function space. These equations are of great importance since they can be used as an approximation for elastic-perfectly plastic Hencky materials

An a posteriori analysis of C\u3csup\u3e0\u3c/sup\u3e interior penalty methods for the obstacle problem of clamped Kirchhoff plates

We develop an a posteriori analysis of C interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error estimator and introduce an adaptive algorithm based on this error estimator. Numerical results indicate that the performance of the adaptive algorithm is optimal for both quadratic and cubic C interior penalty methods. 0 0

Hierarchical error estimates for the energy functional in obstacle problems

We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations

A Posteriori Error Estimates for hphp-FE Discretizations in Elastoplasticity

In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linear kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is conforming with respect to the displacement field and the plastic strain. Furthermore, the paper presents $hp$-finite element discretizations relying on a variational inequality as well as on a mixed variational formulation and discusses their equivalence by using biorthogonal basis functions. Numerical experiments demonstrate the applicability of the theoretical findings and underline the potential of $h$- and $hp$-adaptive finite element discretizations for problems of elastoplasticity.Comment: 20 page