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

Barrenechea, Gabriel and Burman, Erik and Guzman, Johnny (2020) Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow. Mathematical Models and Methods in Applied Sciences, 30 (5). pp. 847-865. ISSN 0218-2025 (https://doi.org/10.1142/S0218202520500165)

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

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