### 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 L2-norm of order O(hk+1/2). We also prove error estimates for the pressure error in the L2-norm.

Original language | English |
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Journal | Mathematical Models and Methods in Applied Sciences |

Publication status | Accepted/In press - 14 Jan 2020 |

### Keywords

- inviscid flows
- well-posedness
- error estimates
- H(div) conforming finite elements

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## Cite this

Barrenechea, G., Burman, E., & Guzman, J. (Accepted/In press). Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow.

*Mathematical Models and Methods in Applied Sciences*.