iterative linear solvers in the context of conservation laws

[ChrisRackauckas]

https://link.springer.com/article/10.1007/s10543-023-00992-w

Q: Do iterative methods (in this case Newton) preserve nonlinear invariants? A: No. Q: What should one do about it? A: Relax the time step but leave the iterations alone.

https://link.springer.com/article/10.1007/s10915-022-01923-7

Q: Do iterative methods preserve basic properties of PDE discretizations such as conservation? A: Some do, some don’t. Q: So if we pick a conservative one, then all is fine? A: No, because consistency is lost (time is slowed down).

https://epubs.siam.org/doi/abs/10.1137/22M1503348

An extension of the previous paper. A bit harder to read but contains some new interesting results, not least on the connection between Krylov methods and pseudotime stepping.

https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202200157

A deeper dive into the inconsistency (time dilation) caused by Krylov methods. I wrote this paper in about 48 hours so it misses a crucial simplification in the main result that I can tell you about if you want to know more.