2025/12/14 by Kedarnath Buda, Buda, Kedarnath, B. V. Rathish Kumar +3
Computer Science · Engineering · #35Q35 #49J20 #49K20 #65N15 #65N30 #76D07 #90C29 #91A10 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #Convergence (economics) #Element (criminal law) #FOS: Mathematics #Finite element method #Mixed finite element method #Nash equilibrium #Optimal control #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability (learning theory) #Stokes problem
paper · pdf · doi:10.48550/arxiv.2512.12561
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/14 · openalex created_date 2025/12/17 · openalex updated_date 2026/08/05
This paper investigates the Nash equilibrium of a bi-objective optimal control problem governed by the Stokes equations. A multi-objective Nash strategy is formulated, and fundamental theoretical results are established, including the existence, uniqueness, and analytical characterization of the equilibrium. A finite element framework is developed to approximate the coupled optimal control system, and the corresponding optimality conditions for both the continuous and discrete formulations are rigorously derived and analyzed. Furthermore, a priori finite element error estimates are obtained for the discrete problem, ensuring convergence and stability of the proposed method. The theoretical results are corroborated by numerical experiments, which demonstrate the accuracy and computational efficiency of the finite element approach.