Robust verification analysis

This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations.