(This text is my reply to an email question in 2011 from a physicist about how to use the words "validation" and "verification" when talking about numerical software.)
##Background:
In the ideal case implementation of software starts from an unambiguous (formal) specification of the problem to be solved. Then the implementation is "just" a matter of refining this specification step by step into something efficiently executable. In practice the specification is often 1) vague, 2) discovered during implementation and 3) changing over time as requirements change.
##Definitions:
- Verification = evaluate whether or not an implementation satisfies a specification
- Validation = make sure that the specification matches the intended requirements
There are often several "levels of abstraction" where the verification at a high level corresponds to validation at the next lower level. This means that the words "validation" and "verification" are sometimes used interchangeably (and similarly "specification" and "implementation") which can be confusing unless the level is spelled out. As an example we could have a case where a PDE + boundary conditions is a specification at a high level (say level 1), then a discretised matrix model is the next level (2), a matlab implementation the third level and a fortran code the lowest level (4).
We can see the matlab code (3) as an implementation with the mathematical matrix model (2) as a specification. Or we can see the matlab code (3) as a specification with the fortran code as the implementation (4).
Similarly the PDE (1) is a specification for the discretised version (2), but also an "implementation" of a physical model (at level 0).