Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint

DOI10.4208/aamm.OA-2020-0302zbMath1499.49013MaRDI QIDQ5032339

Liang Ge, Haifeng Niu, Jian-Wei Zhou

Publication date: 16 February 2022

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

zbMATH Keywords

convergence analysisoptimal controlStokes equationspectral approximation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (6)

Spectral approximation for optimal control problems governed by first bi‐harmonic equation ⋮ Unified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problem ⋮ Two-level iterative finite element methods for the stationary natural convection equations with different viscosities based on three corrections ⋮ A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design ⋮ Unnamed Item ⋮ Approximate controllability of linear parabolic equation with memory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On some control problems in fluid mechanics
• Fast Uzawa algorithm for generalized saddle point problems
• Time-stepping discontinuous Galerkin approximation of optimal control problem governed by time fractional diffusion equation
• Finite element approximation of optimal control problems governed by time fractional diffusion equation
• Legendre-Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension
• State-constrained optimal control of the three-dimensional stationary Navier-Stokes equations
• A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations
• Spectral mixed Galerkin method for state constrained optimal control problem governed by the first bi-harmonic equation
• Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with L²-Norm State-Constraints
• Spectral Methods
• A Legendre–Galerkin Spectral Method for Optimal Control Problems Governed by Stokes Equations
• A Legendre–Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations
• The Convergence Factor of Preconditioned Algorithms of the Arrow–Hurwicz Type
• Boundary Velocity Control of Incompressible Flow with an Application to Viscous Drag Reduction
• A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier--Stokes Equations
• UNIFORM INF–SUP CONDITIONS FOR THE SPECTRAL DISCRETIZATION OF THE STOKES PROBLEM
• Optimal Controls of Navier–Stokes Equations
• Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems
• Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints
• Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
• A Posteriori Error Estimates for Control Problems Governed by Stokes Equations
• An Alternating Direction Method of Multipliers for Optimal Control Problems Constrained with Elliptic Equations
• The Convergence and Superconvergence of a MFEM for Elliptic Optimal Control Problems
• Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations
• Role of the LBB condition in weak spectral projection methods

This page was built for publication: Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint