Adaptive Finite Element Methods for a Class of Evolution Problems in Viscoplasticity

Adaptive finite element procedures are presented for the analysis of broad classes of two-dimensional problems in visco plasticity which involve internal state variables. Several a posteriori error estimates are developed and used as a basis for refinements of meshes of triangular and quadrilateral elements. Algorithms are presented which reduce the computational complexity of the adaptive process and provide for the use of arbitrary local estimates of the approximation error. The resulls of numerical experiments are given which illustrate the effectiveness of the adaptive algorithms and various. error indicators.