  Using the framework of operator or Cald\'{e}ron preconditioning, uniform
preconditioners are constructed for elliptic operators of order $2s \in [0,2]$
discretized with continuous finite (or boundary) elements. The cost of the
preconditioner is the cost of the application an elliptic opposite order
operator discretized with discontinuous or continuous finite elements on the
same mesh, plus minor cost of linear complexity. Herewith the construction of a
so-called dual mesh is avoided.
