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 addition to the displacements, an auxiliary variable, playing the role of a pressure, is introduced resulting in Stokes-like problems. The discretization is done by a stabilized conforming Q1/Q1-element, and the corresponding algebraic systems are solved by an adaptive multigrid scheme using a smoother of block Gauss-Seidel type. The adaptive algorithm is based on the general concept of using duality arguments to obtain weighted a posteriori error bounds. This procedure is carried out here for the described discretization of elasto-plastic problems. Efficiency and reliability of the proposed adaptive method is demonstrated at (plane strain) model problems. (C) 2001, John Wiley & Sons, Inc.