Pressure-Robustness in Stokes-Darcy Optimal Control Problem with Reconstruction Operator

Abstract

This paper presents a pressure-robustness discretization for optimal control problems governed by the Stokes-Darcy system. We revisit the divergence constraint and interface normal continuity within a mixed finite element framework. A reconstruction operator is incorporated into both the constraint equations and the cost functional, together with suitable finite element spaces for approximation and reconstruction. The resulting scheme is pressure-robust. Numerical experiments confirm the theoretical results.