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In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…

Numerical Analysis · Mathematics 2024-02-23 Christian Clason , Vu Huu Nhu , Arnd Rösch

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…

Numerical Analysis · Mathematics 2022-10-06 Dominic Breit , Andreas Prohl

We consider an optimal control problem for the Navier-Stokes system with Navier slip boundary conditions. We denote by $\alpha$ the friction coefficient and we analyze the asymptotic behavior of such a problem as $\alpha\to \infty$. More…

Analysis of PDEs · Mathematics 2019-10-28 Claudia Gariboldi , Takéo Takahashi

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup…

Numerical Analysis · Mathematics 2020-05-25 Woocheol Choi , Young-Pil Choi

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient…

Numerical Analysis · Mathematics 2015-08-27 Eduard Feireisl , Radim Hošek , David Maltese , Antonín Novotný

A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are…

Optimization and Control · Mathematics 2013-10-23 Elder J. Villamizar-Roa , Elva Ortega-Torres

This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…

Numerical Analysis · Mathematics 2017-05-29 Javier de Frutos , Bosco García-Archilla , Volker John , Julia Novo

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…

Optimization and Control · Mathematics 2018-03-12 Luis H. R. Alvarez E.

We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…

Computation · Statistics 2026-02-04 Nicholas Polson , Vadim Sokolov

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…

Numerical Analysis · Mathematics 2020-11-25 Christian Meyer , Monika Weymuth

A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…

Numerical Analysis · Mathematics 2026-04-28 Muhammad Afzal , Naveed Ahmed , Volker John

This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

Optimization and Control · Mathematics 2010-05-19 Hanbing Liu

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

Numerical Analysis · Mathematics 2019-11-22 Alejandro Allendes , Francisco Fuica , Enrique Otarola , Daniel Quero

A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…

Numerical Analysis · Mathematics 2025-01-15 Nils Bullerjahn , Balázs Kovács

The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…

Numerical Analysis · Mathematics 2026-02-09 María Gabriela Armentano , Mauricio Mendiluce

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…

Optimization and Control · Mathematics 2018-10-30 Peter Benner , Christoph Trautwein

We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…

Optimization and Control · Mathematics 2015-11-05 Nadir Arada , Fernanda Cipriano