Question

Order of accuracy m means _____________

(a) as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m powers of the grid size

(b) as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m times of the grid size

(c) as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m powers of the grid size

(d) as the grid size is reduced, the approximations diverge from the exact solution with an error proportional to m times of the grid size

This question was addressed to me in an interview.

This key question is from Finite Difference Method in chapter Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Correct choice is (a) as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m powers of the grid size

Easiest explanation: An order of accuracy m means that the truncation error starts with a term proportional to grid size^m. So, the statement “as the grid size is reduced, the approximations converge to the exact solution with an error proportional to m powers of the grid size” is correct.