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Grad-Div Stabilization for Approximating Control of Thermally Convective Flows With Mixed Finite Elements
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DOI：10.1002/num.70069.png)
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Abstract
En 中文
We investigate approximating control of viscous incompressible thermally convective flows using inf-sup stable mixed finite elements with grad-div stabilization. The proposed method augments the Galerkin finite element method with a grad-div stabilization term enhancing mass conservation and improving the performance of the algorithm. We analyse a mixed finite element method-based semi-discretization of the grad-div stabilized optimality system from which optimal control can be computed. An optimal order error estimate of the approximations of the optimality system is derived in and L infinity(L-2)and L infinity(H-1)-norms without nonlocal compatibility conditions. Numerical results are presented by solving a control problem that involves minimizing vorticity in a mixed convective flow past a backward-facing step channel. Numerical experiments show the feasibility and applicability of the grad-div stabilization for approximating control of thermally convective flows with mixed finite elements.
Keywords:
boundary control
Boussinesq equations
grad-div stabilization
heat transfer
inf-sup stable finite elements
optimality system
Journal
N
IF:
1.7
Papers:
46
Citations:
3.9K
