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

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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 [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.