On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations

DOI10.1007/s10915-016-0266-xzbMath1401.76086OpenAlexW2508513047MaRDI QIDQ520211

Arnaud Münch, Diego A. Souza, Enrique Fernández-Cara

Publication date: 3 April 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-016-0266-x

zbMATH Keywords

heat equationnumerical methodsmixed finite elementsnull controllabilityStokes and Navier-Stokes equations

Mathematics Subject Classification ID

Controllability (93B05) Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (10)

Local null-controllability for some quasi-linear phase-field systems with Neumann boundary conditions by one control force ⋮ Local null controllability of a class of non-Newtonian incompressible viscous fluids ⋮ Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence ⋮ Constructive exact control of semilinear 1D heat equations ⋮ Local null controllability of a quasi-linear system and related numerical experiments ⋮ On the theoretical and numerical control of a one-dimensional nonlinear parabolic partial differential equation ⋮ Numerical Stackelberg--Nash Control for the Heat Equation ⋮ Space-time least-squares finite elements for parabolic equations ⋮ RBF collocation and hybrid-LHI methods for Stokes systems and its application to controllability problems ⋮ Numerical reconstruction based on Carleman estimates of a source term in a reaction–diffusion equation

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical exact controllability of the 1D heat equation: duality and Carleman weights
• Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition
• Carleman estimates for parabolic equations with nonhomogeneous boundary conditions
• On exact and approximate boundary controllabilities for the heat equation: A numerical approach
• Handbook of Numerical Analysis IX. Numerical methods for fluids (Part 3)
• Numerical null controllability of semi-linear 1-D heat equations: fixed point, least squares and Newton methods
• Local exact controllability of the Navier-Stokes system
• Strong convergent approximations of null controls for the 1D heat equation
• A least-squares formulation for the approximation of controls for the Stokes system
• On the observability of abstract time-discrete linear parabolic equations
• Uniform controllability of semidiscrete approximations of parabolic control systems
• Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation
• Remarks on exact controllability for the Navier-Stokes equations
• On the Dirichlet boundary controllability of the one-dimensional heat equation: semi-analytical calculations and ill-posedness degree
• On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems
• The Convergence Factor of Preconditioned Algorithms of the Arrow–Hurwicz Type
• Mixed and Hybrid Finite Element Methods
• Perspectives in Flow Control and Optimization
• New development in freefem++
• Numerical null controllability of the heat equation through a least squares and variational approach
• Numerical controllability of the wave equation through primal methods and Carleman estimates
• Inverse problems for linear hyperbolic equations using mixed formulations
• A mixed formulation for the direct approximation of \(L^2\)-weighted controls for the linear heat equation

This page was built for publication: On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations