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arXiv · 1907.05699

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

Gabriel Barrenechea·Erik Burman·Johnny Guzmàn
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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.

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Gabriel Barrenechea, Erik Burman, Johnny Guzmàn. 2019-12-06. Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow. https://arxiv.org/abs/1907.05699

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