  The stability properties of simple element choices for the mixed formulation
of the Laplacian are investigated numerically. The element choices studied use
vector Lagrange elements, i.e., the space of continuous piecewise polynomial
vector fields of degree at most r, for the vector variable, and the divergence
of this space, which consists of discontinuous piecewise polynomials of one
degree lower, for the scalar variable. For polynomial degrees r equal 2 or 3,
this pair of spaces was found to be stable for all mesh families tested. In
particular, it is stable on diagonal mesh families, in contrast to its
behaviour for the Stokes equations. For degree r equal 1, stability holds for
some meshes, but not for others. Additionally, convergence was observed
precisely for the methods that were observed to be stable. However, it seems
that optimal order L2 estimates for the vector variable, known to hold for r>3,
do not hold for lower degrees.
