  A numerical method is presented which conveniently computes upper bounds on
heat transport and poloidal energy in plane layer convection for infinite and
finite Prandtl numbers. The bounds obtained for the heat transport coincide
with earlier results. These bounds imply upper bounds for the poloidal energy
which follow directly from the definitions of dissipation and energy. The same
constraints used for computing upper bounds on the heat transport lead to
improved bounds for the poloidal energy.
