Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds

We present a technique for the evaluation of linear‐functional outputs of parametrized elliptic partial differential equations in the context of deployed (in service) systems. Deployed systems require real‐time and certified output prediction in support of immediate and safe (feasible) action. The two essential components of our approach are (i) rapidly, uniformly convergent reduced‐basis approximations, and (ii) associated rigorous and sharp a posteriori error bounds; in both components we exploit affine parametric structure and offline–online computational decompositions to provide real‐time deployed response. In this paper we extend our methodology to the parametrized steady incompressible Navier–Stokes equations.

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