Pressure-robustness in Stokes-Darcy Optimal Control Problem with reconstruction operator

TL;DR

This paper develops a pressure-robust discretization method for the Stokes-Darcy optimal control problem using a reconstruction operator and specialized finite element spaces, improving numerical stability and accuracy.

Contribution

It introduces a novel pressure-robust discretization scheme employing a reconstruction operator within the mixed finite element framework for Stokes-Darcy optimal control.

Findings

Enhanced pressure-robustness in discretization

Improved numerical stability and accuracy

Effective use of reconstruction operator in FEM

Abstract

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement of normal continuity at interfaces, within the framework of the mixed finite element method (FEM). The methodology involves the strategic deployment of a reconstruction operator, which is adeptly applied to both the constraint equations and the cost functional. This is complemented by a judicious selection of finite element spaces that are tailored for approximation and reconstruction purposes. The synergy of these methodological choices leads to the realization of a discretization scheme that is pressure-robust, thereby enhancing the robustness and reliability of numerical simulations in computational mathematics.