  For numerical approximation the reformulation of a PDE as a residual
minimisation problem has the advantages that the resulting linear system is
symmetric positive definite, and that the norm of the residual provides an a
posteriori error estimator. Furthermore, it allows for the treatment of general
inhomogeneous boundary conditions. In many minimal residual formulations,
however, one or more terms of the residual are measured in negative or
fractional Sobolev norms. In this work, we provide a general approach to
replace those norms by efficiently evaluable expressions without sacrificing
quasi-optimality of the resulting numerical solution. We exemplify our approach
by verifying the necessary inf-sup conditions for four formulations of a model
second order elliptic equation with inhomogeneous Dirichlet and/or Neumann
boundary conditions. We report on numerical experiments for the Poisson problem
with mixed inhomogeneous Dirichlet and Neumann boundary conditions in an
ultra-weak first order system formulation.
