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This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative…

Numerical Analysis · Mathematics 2025-10-10 Xiaobing Feng , Liet Vo

In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…

Optimization and Control · Mathematics 2024-10-02 Telma Guerra , Irene Marín-Gayte , Jorge Tiago

We provide optimal order pressure error estimates for the Crank-Nicolson semidiscretization of the incompressible Navier-Stokes equations. Second order estimates for the velocity error are long known, we prove that the pressure error is of…

Numerical Analysis · Mathematics 2020-08-11 Florian Sonner , Thomas Richter

We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration…

Numerical Analysis · Mathematics 2023-08-29 Aaron Brunk , Herbert Egger , Oliver Habrich , Maria Lukacova-Medvidova

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…

Analysis of PDEs · Mathematics 2026-02-12 Buddhika Priyasad , Sérgio S. Rodrigues

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…

Numerical Analysis · Mathematics 2018-10-08 Alejandro Allendes , Francisco Fuica , Enrique Otárola , Daniel Quero

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

Numerical Analysis · Mathematics 2023-01-16 Erik Burman , Deepika Garg , Janosch Preuss

In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different…

Optimization and Control · Mathematics 2018-09-19 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

Numerical Analysis · Mathematics 2025-04-16 Santolo Leveque , Michele Benzi , Patrick E. Farrell

In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to accommodate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations.…

Numerical Analysis · Mathematics 2025-01-27 Aparna Bansal , Nicolás Barnafi , Rodolfo Araya , Dwijendra Narain Pandey

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty,…

Analysis of PDEs · Mathematics 2023-12-12 Nikolai Chemetov , Fernanda Cipriano

We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…

Numerical Analysis · Mathematics 2010-11-01 Thierry Gallouët , Laura Gastaldo , Jean-Claude Latché , Raphaele Herbin

In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…

Optimization and Control · Mathematics 2016-01-21 Nadir Arada , Fernanda Cipriano

In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…

Optimization and Control · Mathematics 2017-05-04 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear…

Numerical Analysis · Mathematics 2016-12-23 Javier de Frutos , Bosco García-Archilla , Julia Novo

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data…

Analysis of PDEs · Mathematics 2021-06-07 Elisabeth Diehl , Johannes Haubner , Michael Ulbrich , Stefan Ulbrich

In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional…

Optimization and Control · Mathematics 2020-07-09 Eduardo Casas , Karl Kunisch