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

2019/07/12 by Barrenechea, Gabriel, Burman, Erik, Guzmàn, Johnny · 1 citation
#35Q35 #65N12 #65N15 #76M10 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1907.05699

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(h^k+\frac12). We also prove error estimates for the pressure error in the L²-norm.

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• A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows

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