Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations

DOI10.1007/s10589-014-9649-9zbMath1297.49047OpenAlexW2014592335MaRDI QIDQ457234

Gang Chen, Min-Fu Feng

Publication date: 26 September 2014

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-014-9649-9

zbMATH Keywords

optimal controlfinite elementssmall viscosityReynolds numberLBB stability conditionsubgrid scale eddy viscosityunsteady Oseen equations

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items

A projection-based variational multiscale method for the optimal control problems governed by the stationary Navier-Stokes equations ⋮ Semi-discrete a priori error analysis for the optimal control of the unsteady Navier-Stokes equations with variational multiscale stabilization ⋮ The effect of a sparse Grad-div stabilization on control of stationary Navier-Stokes equations

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite element methods for linear hyperbolic problems
• A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
• Approximation of a class of optimal control problems with order of convergence estimates
• Subgridscale stabilization of time-dependent convection dominated diffusive transport
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• A finite element pressure gradient stabilization for the Stokes equations based on local projections
• A connection between subgrid scale eddy viscosity and mixed methods
• Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
• A new absolutely stable simplified Galerkin least-squares finite element method using nonconforming element for the Stokes problem
• Finite element error analysis of a variational multiscale method for the Navier-Stokes equations
• Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales
• A New Stabilized Subgrid Eddy Viscosity Method Based on Pressure Projection and Extrapolated Trapezoidal Rule for the Transient Navier-Stokes Equations
• A unified convergence analysis for local projection stabilisations applied to the Oseen problem
• Streamline Diffusion Methods for the Incompressible Euler and Navier-Stokes Equations
• On the approximation of the solution of an optimal control problem governed by an elliptic equation
• Finite Element Approximation of Parabolic Time Optimal Control Problems
• Convergence of Finite Element Approximations to State Constrained Convex Parabolic Boundary Control Problems
• Optimal control in fluid mechanics by finite elements with symmetric stabilization
• Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
• New development in freefem++
• A Least Squares Petrov-Galerkin Finite Element Method for the Stationary Navier-Stokes Equations
• Galerkin Finite Element Methods with Symmetric Pressure Stabilization for the Transient Stokes Equations: Stability and Convergence Analysis
• Stabilization of Low-order Mixed Finite Elements for the Stokes Equations