A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations (Q1996227)

Usually, if there is known that a PDE problem possesses a sufficiently regular solution, then convergence of some numerical methods applied to that problem is guaranteed. The author shows that a reverse implication in the case of Navier-Stokes equations in three-dimensional polyhedral domains holds true. Namely, if a numerical solution is bounded in a certain norm for a sufficiently small mesh, then the system has a unique smooth solution which is well approximated by numerical solutions.