Abstract
AbstractIn 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. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:369–382, 2001
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