Linear and Nonlinear Boundary Conditions: What's the difference?
Abstract
In previous work, we derived new energy and entropy stable open boundary conditions and implementation procedures for linear and nonlinear initial boundary value problems. These boundary procedures results 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 both linear and nonlinear initial boundary value problems and can be implemented both strongly and weakly.
Cite
@article{arxiv.2509.11651,
title = {Linear and Nonlinear Boundary Conditions: What's the difference?},
author = {Jan Nordström},
journal= {arXiv preprint arXiv:2509.11651},
year = {2025}
}
Comments
Presented at ICOSAHOM 2025, 13 - 18 July Montreal, Canada, The 15th International Conference on Spectral and High Order Methods