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

Gabriel Barrenechea; Erik Burman; Johnny Guzman

doi:10.1142/S0218202520500165

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

Gabriel Barrenechea, Erik Burman, Johnny Guzman

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	847-865
Number of pages	19
Journal	Mathematical Models and Methods in Applied Sciences
Volume	30
Issue number	5
DOIs	https://doi.org/10.1142/S0218202520500165
Publication status	Published - 31 May 2020

Keywords

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

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Barrenechea-etal-MMMAS-2020-Well-posedness-and-H-div-conforming-finite-element-approximation-of-a-linearisedAccepted author manuscript, 390 KB

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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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AU - Barrenechea, Gabriel

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AU - Guzman, Johnny

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Y1 - 2020/5/31

N2 - 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.

AB - 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.

KW - inviscid flows

KW - well-posedness

KW - error estimates

KW - H(div) conforming finite elements

UR - https://www.worldscientific.com/loi/m3as

U2 - 10.1142/S0218202520500165

DO - 10.1142/S0218202520500165

M3 - Article

VL - 30

SP - 847

EP - 865

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 5

ER -

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

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