An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials

In this article, a mixed finite element formulation is described for coping with (nearly) incompressible behavior in elasto-plastic problems. In addit ion to the displacements, an auxiliary variable, playing the role of a pres sure, is introduced resulting in Stokes-like problems. The discretization i s done by a stabilized conforming Q1/Q1-element, and the corresponding alge braic systems are solved by an adaptive multigrid scheme using a smoother o f block Gauss-Seidel type. The adaptive algorithm is based on the general c oncept of using duality arguments to obtain weighted a posteriori error bou nds. This procedure is carried out here for the described discretization of elasto-plastic problems. Efficiency and reliability of the proposed adapti ve method is demonstrated at (plane strain) model problems. (C) 2001, John Wiley & Sons, Inc.