## Joseph M. Powers - Verification in Scientific Computing: from Pristine to Practical to Perimeter-Extending

*Methods of verification of predictions from scientific computing will be surveyed. Verification, sometimes characterized as “solving the equations right,” is often more amenable to mathematical methods than its equally important counterpart, validation, characterized as “solving the right equations.” First focus will be given to a variety of standard verification methods used in compressible and reactive fluid mechanics; these can be characterized as “pristine” and typically involve demonstration of how error norms converge as a function of discretization and comparison to asymptotic convergence rates. Prediction of such flows can be challenging to verify because of the vast disparity of length and time scales inherent in such flows. The pres - ence of thin viscous and reaction layers, surfaces of discontinuity found in inviscid limits, and inherent insta- bility each represent challenges to achieving verified solutions. Often however, one is faced with more prac- tical problems in verification, especially for cases where computational resources are scarce or the dynamics are such that it is difficult to define a normed error. For such cases, discussion will be presented of how com - putational scientists, as well as those that review the science, can practically address the topic of verification. Finally, discussion will be given as to how to expand the perimeter of what can be verified, especially with regard to problems that exhibit spatio-temporal instability, nonlinear dynamics, and transition to chaos.*

11/12/2023