Discontinuous Galerkin methods for the incompressible flow with nonlinear leak boundary conditions of friction type

This work aims at employing the discontinuous Galerkin (DG) methods for the incompressible flow with nonlinear leak boundary conditions of friction type, whose continuous variational problem is an inequality due to the subdifferential property of such boundary conditions. Error estimates are derived for the velocity and pressure in the corresponding norms, this work ends with numerical results to demonstrate the theoretically predicted convergence orders and reflect the leak or non-leak phenomena.