A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity

A new approach to a posteriori error estimation and adaptive mesh design based on techniques from optimal control is presented for primal-mixed finite element models in elasto-plasticity. This method uses global duality arguments for deriving weighted a posteriori error bounds for arbitrary functionals of the error representing physical quantities of interest. In these estimates local residuals of the computed solution are multiplied by certain weights which are obtained by solving a linearized global dual problem numerically. The resulting local error indicators are used in a feed-back process for generating economical meshes. This approach is developed here for the Hencky and Prandtl-Reuss models in linear-elastic perfect plasticity. Its performance is demonstrated for a plane-strain benchmark problem.

[1]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[2]  Alain Bensoussan,et al.  Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and $H^{1}$ regularity , 1996 .

[3]  Claes Johnson,et al.  Adaptive finite element methods in computational mechanics , 1992 .

[4]  W. Rheinboldt,et al.  Error Estimates for Adaptive Finite Element Computations , 1978 .

[5]  Rolf Rannacher,et al.  A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity , 1998 .

[6]  Kenneth Eriksson,et al.  An adaptive finite element method for linear elliptic problems , 1988 .

[7]  Willy Dörfler,et al.  An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation , 1998, Math. Comput..

[8]  R. Bank,et al.  Some a posteriori error estimators for elliptic partial differential equations , 1985 .

[9]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[10]  R. RannacherInstitut,et al.  Weighted a Posteriori Error Control in Fe Methods , 1995 .

[11]  L. Franca,et al.  Error analysis of some Galerkin least squares methods for the elasticity equations , 1991 .

[12]  R. Rannacher,et al.  A feed-back approach to error control in finite element methods: application to linear elasticity , 1997 .

[13]  Rolf Rannacher,et al.  A Feed-Back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples , 1996 .

[14]  Th. Lehmann,et al.  On the coupled thermo-mechanical process in the necking problem , 1985 .

[15]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .