Linear and nonlinear boundary conditions: What’s the difference?

In previous work, we derived new energy and entropy stable open boundary conditions and implementation techniques for linear and nonlinear initial boundary value problems. These boundary procedures result in estimates bounded by external data only. Interestingly, these new boundary conditions generalize the well-known classical characteristic boundary conditions for linear problems to the nonlinear setting. We discuss the similarities and differences between these two boundary procedures and point out the advantages with the new procedures. In particular we show that the new boundary conditions bound solutions to both linear and nonlinear initial boundary value problems and can be implemented both strongly and weakly.