  We consider boundary element methods where the Calder\'on projector is used
for the system matrix and boundary conditions are weakly imposed using a
particular variational boundary operator designed using techniques from
augmented Lagrangian methods. Regardless of the boundary conditions, both the
primal trace variable and the flux are approximated. We focus on the imposition
of Dirichlet, mixed Dirichlet--Neumann, and Robin conditions. A salient feature
of the Robin condition is that the conditioning of the system is robust also
for stiff boundary conditions. The theory is illustrated by a series of
numerical examples.

Numerical Analysis