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The concepts of Verification and Validation (V&V) can be oversimplified in a succinct manner by saying that “verification is doing things right” and “validation is doing the right thing”. In the world of the Finite Element Method (FEM) and computational analysis, it is sometimes said “verification means solving the equations right” and “validation means solving the right equations”. In other words, if one intends to give an answer to the equation “2+2=”, then one must run the resulting code to assure that the answer “4” results. However, if the nature of the physics or engineering problem being addressed with this code is multiplicative rather than additive, then even though Verification may succeed (2+2=4 etc), Validation will fail because the equations coded are not those needed to address the real world (multiplicative) problem.

The implementation of Verification and Validation (V&V) of a computational model of a physical system can be simply described as a 4-step process. One of the steps in the 4-step process is that of Solution Verification. Solution Verification is the process of assuring that a model approximating a physical reality with a discretized continuum (e.g. finite element) code converges in each discretized domain to a converged answer on the quantity of validation interest. The modeling reality is that often we are modeling a problem with a discretized code because it is neither smooth nor continuous spatially (e.g. contact and impact) or in relevant physics (e.g. shocks, melting, etc). The typical result is a non-monotonic convergence plot that can lead to spurious conclusions about the order of convergence, and a lack of means to estimate residual error or uncertainty.