Goal-Oriented Adaptive Finite Element Analysis in Computational Material Mechanics

Doctoral thesis, 2003

This thesis is concerned with error control in computational material mechanics. A posteriori error estimation and adaptivity for finite element discretizations is investigated. Based on the technique of solving a dual problem, it is possible to control the accuracy of arbitrary quantities. Strategies for goal-oriented error estimation and adaptivity, with respect to user-defined error measures, are presented. Application is made to problems of elasticity, thermoelasticity and viscoplasticity, where special attention is made to the rate independent limit case of plasticity. A quite general framework for a posteriori error estimation is proposed for problems where the (dissipative) material behavior is modeled using internal variables. In particular, it is investigated how the accuracy of the error estimate is affected by different approaches for solving the dual problem. Methods for computing the dual solution in space, time, and coupled space-time domains are presented. Moreover, adaptive strategies based on these estimators are proposed for spatial and temporal problems.