Question

Which of these is related to convergence?

(a) Stopping criteria

(b) Peclet number

(c) Lax Equivalence Theorem

(d) Scarborough criteria

This question was posed to me by my school principal while I was bunking the class.

I want to ask this question from Discretization Aspects in portion Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

The correct answer is:

(a) Stopping criteria

Explanation:

• Stopping criteria is directly related to convergence in numerical methods. It is used to determine when an iterative solver should stop based on a specified threshold or when the solution has sufficiently converged. Convergence refers to the process by which a numerical solution approaches the exact solution as the number of iterations increases.

• Peclet number (b) is a dimensionless number that characterizes the relative importance of convective and diffusive transport in a flow. While it is important for analyzing convection-diffusion problems, it does not directly relate to convergence.

• Lax Equivalence Theorem (c) is a theorem in numerical analysis that relates the consistency and stability of a numerical scheme to its convergence. It is important for understanding the theoretical foundation of convergence but is not directly a measure or criterion for convergence.

• Scarborough criteria (d) are used for assessing the stability of certain numerical methods, especially in the context of finite difference schemes. It is not specifically focused on convergence.

Thus, stopping criteria is the most directly related to convergence.