Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

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 L2-norm of order O(hk+12). We also prove error estimates for the pressure error in the L2-norm