The paper presents a local-form continuum sensitivity analysis approach to the incompressible Navier-Stokes equations. The Navier-Stokes equations are discretized using the Qi-Q Taylor-Hood elements which are the minimum order elements required for local-form sensitivity analysis without needing solution reconstruction. The method is used to calculate the solution and sensitivities of a benchmark problem and the results are verified. The sensitivity analysis results for local sensitivities exhibit second order convergence with mesh refinement. The material sensitivities on the other hand exhibit only first order convergence due to the first order convergence of the spatial gradients in the convective term. Finally the effect of mesh parameters on the sensitivity results indicates that the mesh adaptation for sensitivity analysis is different from that for flow analysis.
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