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arXiv · 2403.15783

Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity

Harpal Singh·Arbaz Khan
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Abstract

This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized Oseen equations. We provide optimal a priori error estimates in energy norms for such problems using the divergence-conforming DGFEM approach. Moreover, we thoroughly analyze $L^2$ error estimates for scenarios dominated by diffusion and convection. Additionally, we establish the new reliable and efficient a posteriori error estimators for the optimal control of the Oseen equation with variable viscosity. Theoretical findings are validated through numerical experiments conducted in both two and three dimensions.

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Harpal Singh, Arbaz Khan. 2024-03-23. Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity. https://doi.org/10.1137/24m1649824

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