stop criterion discussion
 

Hi Foamers,

in these days of quarantine I was wandering about the residuals stop criterion used in solvers. In particular I'm talking about steady state solvers.

For what I understood until now about OpenFOAM, the finite volume method implemented in it for solving Navier-Stokes, or just Stokes, equations is a P1-P1 scheme that doesn't respect the discrete inf-sup condition.
For this reason, we have an iterative algorithm that solves at each iteration a relaxed equation.
Another non-linearity is introduced if we have a non-orthogonal mesh because non-orthogonal part is taken explicitly.

These thoughts made me think about OpenFOAM solver as a fixed point iterative method for almost every equation one can consider, both linear and non-linear.

By basic numerical mathematics we know that stop criterions based on residual are affected by the derivative of the non-linear scheme in the zero: if it is not near 1 we have over/under estimation of the error.

On the other hand we know that increment-based criterions get worse only when the derivative is near one (but over estimating the error).

So, has anyone ever try to use increment to estimate the solution error?

I hope you understand my doubts!
Thanks in advance