We introduce and study an adaptive finite element method for
nonlinear variational problems associated with multivalued
operators. This formulation writes the problem in terms of the
unknown variable and an extra Lagrange multiplier. The algorithm
consists of an Uzawa outer iteration to update the Lagrange
multiplier and an elliptic inner iteration for the unknown that is solved
using Adaptive FEM. We show linear convergence for the pairs of the finite
element spaces. We particularize the results (apply the method) for two
specific examples: the Elasto-Plastic Torsion Problem and a
Bingham fluid in a Cylindrical Pipe. The numerical experiments
were developed with the ALBERTA FEM toolbox.