[01946] Optimal Control of Stationary Doubly Diffusive Flows on Lipschitz Domains
Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
Type : Contributed Talk
Abstract : Doubly diffusive flows involve coupled incompressible flow and double diffusion transport, which models physical problems like bacteria bioconvection, exothermic flows in oceanography and more. We study a distributed optimal control problem governed by doubly diffusive flows under minimal regularity on 2D and 3D bounded Lipschitz domains and establish its well-posedness. First and second-order optimality conditions are derived. Furthermore, a discretization of the control problem based on $H(\mbox{div})$-conforming discontinuous Galerkin finite elements for the state and adjoint variables and piecewise constant finite elements for the control variable is discussed. Optimal apriori error estimates are proven in suitable norms. Numerical experiments are performed using a semi-smooth Newton strategy verifying the theoretical findings.
