The approximation of boundary control problems for fluid flows with an application to control by heating and cooling
The method of Lagrange multipliers is used to derive a system of partial differential equations whose solutions provide the optimal states and controls. No simplifications concerning the flow are invoked, i.e. the full Navier-Stokes equations are employed. Finite element algorithms for approximating the optimal states and controls are discussed, as is the accuracy of approximations resulting from these algorithms. Details are provided for the example of using heating and cooling controls in order to avoid hot spots along bounding surfaces.
scientific article; zbMATH DE number 429005