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Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow

Monika Neda, Faranak Pahlevani, Leo G. Rebholz and Jiajia Waters

Abstract

We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and non-isothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.

Funding

The work of the third author was partially supported by NSF grant DMS1112593.

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Received: 2015-1-30
Revised: 2015-4-22
Accepted: 2016-4-24
Published Online: 2016-10-5
Published in Print: 2016-10-1

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