In the present paper we compute upper and lower bounds for limit analysis in two and three dimensions. From the solution of the discretised upper and lower bound problems, and from the optimum displacement rate and stress fields, we compute an error estimate defined at the body elements and at their boundaries, which are applied in an adaptive remeshing strategy. In order to reduce the computational cost in 3D limit analysis, the tightness of the upper bound is relaxed and its computation avoided. Instead, the results of the lower bound are used to estimate elemental and edge errors. The theory has been implemented for Von Mises materials, and applied to two- and three-dimensions examples.