Analysis and approximation of the Cross model for quasi-Newtonian flows with defective boundary conditions

•A defective boundary condition problem is approximated by an optimization approach.•The control problem is analyzed for an existence result and the Lagrange multipliers.•Numerical experiments verify robustness of the developed decoupling algorithm.

A numerical method for a generalized-Newtonian fluid with flow rate boundary conditions is considered. The defect boundary condition problem is formulated as a constrained optimal control problem, where a flow balance is forced on the inflow and outflow boundaries using a Neumann control. The control problem is analyzed for an existence result and the Lagrange multiplier rule. A decoupling solution algorithm is presented and numerical experiments are provided to validate robustness of the algorithm.