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

## TL;DR

This paper establishes the well-posedness of a linearised inviscid flow model and develops H(div)-conforming finite element methods, providing error estimates for velocity and pressure approximations.

## Contribution

It introduces a regularisation approach for the model and proves error bounds for finite element discretisations, advancing numerical analysis of inviscid flow models.

## Key findings

- Existence and uniqueness of weak solutions for smooth domains.
- Error estimate of order O(h^{k+1/2}) for velocity in L2-norm.
- Error estimates for pressure in L2-norm.

## Abstract

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.