A near-optimal recovery algorithm for the Stokes equations with incomplete information on the boundary conditions
It provides a rigorous recovery method for fluid dynamics problems where boundary conditions are partially unknown, which is a common issue in practical applications.
The paper proposes an algorithm for approximating velocity and pressure in Stokes equations with incomplete boundary conditions, using linear measurements to achieve a near-optimal solution in energy norm.
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not uniquely determine the velocity-pressure couple. We propose an algorithm that takes advantage of available linear measurements of the velocity and pressure to construct a numerical approximation. This approximation is guaranteed to be near-optimal in the sense that it approximates the velocity-pressure couple that minimizes, in the energy norm, the distance to all other solutions satisfying the measurements and the Stokes system.