  We consider a linearised model of incompressible inviscid flow. Using a
regularisation based on the Hodge Laplacian we prove existence and uniqueness
of weak solutions for smooth domains. The model problem is then discretised
using H(div)-conforming finite element methods, for which we prove error
estimates for the velocity approximation in the $L^2$-norm of order
$O(h^{k+\frac12})$. We also prove error estimates for the pressure error in the
$L^2$-norm.
