Least squares approach for the time-dependent nonlinear Stokes–Darcy flow

A time-dependent nonlinear model of Stokes–Darcy flows is considered for numerical approximations by an optimization based domain decomposition method. The coupled system is formulated as a constrained optimal control problem, where a Neumann type control is introduced to enforce boundary conditions on the interface of subdomains. A computational algorithm is discussed for the least squares functional which measures the jump of flow balance across the interface. Numerical results are presented to validate convergence and accuracy of the method.