Question

Stability is defined _________

(a) only for iterative solvers

(b) only for direct solvers

(c) for all numerical solvers

(d) for all discretization processes

The question was posed to me during an online exam.

My question comes from Discretization Aspects topic in portion Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

The correct answer is:

(c) for all numerical solvers

Stability is a fundamental concept in numerical methods that applies to both iterative and direct solvers. It refers to the behavior of the solution as the computation progresses, ensuring that errors do not grow uncontrollably over time. Stability is important for ensuring the accuracy and reliability of the numerical solution, and it is considered for all types of solvers and discretization processes used in computational fluid dynamics.