Question

What happens when the convergence is not monotonic?

(a) Solutions will always converge

(b) Solutions will not converge

(c) Erroneous solutions may converge

(d) Error will increase

I had been asked this question during an online interview.

Enquiry is from Errors in Finite Difference Approximations topic in portion Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Correct option is (c) Erroneous solutions may converge

To explain: The order of convergence is valid only when the convergence is monotonic. This is because, for two consecutive grids, results may also converge even if the error is large. Then, a third grid arrangement must be used to assure the real convergence of the solution.