Before revision:  Results have also been presented for the handling of grids with hanging nodes for higher-order Lagrange elements. Numerical simulation illustrating the satisfaction and the violation of  discrete maximum principle (DMP) for the BJK limiter and the Kuzmin limiter, respectively have been presented in two dimensions.
After revision:  Numerical simulations illustrating the satisfaction and the violation of discrete maximum principle (DMP) for the BJK limiter and the Kuzmin limiter, respectively have been presented in two dimensions.