Process of checking that a computational implementation correctly and accurately solves the intended mathematical model, free of coding mistakes, numerical errors, or algorithmic inconsistencies.

Principle

Demonstrate that the numerical methods and code reproduce known solutions, converge with resolution, and satisfy conservation or consistency properties; use unit tests, manufactured solutions, and code reviews.

Demonstration

A finite-element heat-transfer solver is verified by reproducing an analytic temperature distribution and by demonstrating expected convergence rates as the mesh is refined.

Misapplication

Treating successful verification as proof the model represents reality, skipping verification because the results 'look reasonable', or using ad hoc checks that do not exercise critical code paths.

Consequence

Proper verification reduces the risk of undetected implementation errors, provides reproducible tests that guard against regressions, and increases confidence in subsequent validation and uncertainty analysis.

Reversal

Failure of verification exposes coding or numerical flaws that invalidate any conclusions drawn from the implementation; confusing verification with validation leads to misplaced trust.

Boundary

Verification addresses correctness of the implementation relative to the mathematical specification; it does not test the adequacy of the model form, parameter choices, or real‑world predictive ability.

Semantic Tension

Tension arises with validation and calibration when terminology is loose; verification is often mistaken for validation or omitted under time pressure.

Synthesis

Model verification is the systematic assurance that the code and algorithms faithfully solve the stated mathematical model, forming the technical foundation for later validation and analysis.