A uniformly controllable and implicit scheme for the 1-D wave equation

DOI10.1051/m2an:2005012zbMath1130.93016OpenAlexW2006022800MaRDI QIDQ5315511

Arnaud Münch

Publication date: 8 September 2005

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2005__39_2_377_0

Mathematics Subject Classification ID

Controllability (93B05) Initial-boundary value problems for second-order hyperbolic equations (35L20) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items

Uniform polynomial observability of time-discrete conservative linear systems, Exact controllability of a piezoelectric body. Theory and numerical simulation, Observability for the Wave Equation with Variable Support in the Dirichlet and Neumann Cases, Numerical Control of a Semilinear Wave Equation on an Interval, Quasi exponential decay of a finite difference space discretization of the 1-d wave equation by pointwise interior stabilization, Uniformly controllable schemes for the wave equation on the unit square, Boundary observability of a numerical approximation of Maxwell's system in a cube, Approximation of controls for linear wave equations: a first order mixed formulation, Best decay rate, observability and open-loop admissibility costs: discussions and numerical study, Numerical observers with vanishing viscosity for the 1d wave equation, An application of moment method to uniform boundary controllability property of a semidiscrete 1-d wave equation with a lower rate vanishing viscosity, Spacetime finite element methods for control problems subject to the wave equation, Optimal location of the support of the control for the 1-D wave equation: numerical investigations, Control of partial differential equations via physics-informed neural networks, On the observability of time-discrete conservative linear systems, A mixed formulation for the direct approximation of the control of minimal \(L^2\)-norm for linear type wave equations, Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes, A variational method for the numerical simulation of a boundary controllability problem for the linear and semilinear 1D wave equations, Uniform stabilization of a viscous numerical approximation for a locally damped wave equation, Optimal design of the support of the control for the 2D wave equation, Space time stabilized finite element methods for a unique continuation problem subject to the wave equation, Singular asymptotic expansion of the exact control for the perturbed wave equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary controllability of a linear semi-discrete 1-D wave equation derived from a mixed finite element method
• Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation
• Boundary observability for the finite-difference space semi-discretizations of the 2-D wave equation in the square
• Convergence of a multigrid method for the controllability of a 1-D wave equation.
• Discrete Ingham inequalities and applications.
• Uniform boundary controllability of a semi-discrete 1-D wave equation
• Family of implicit schemes uniformly controllable for the 1-D wave equation.
• Uniform boundary controllability of a discrete 1-D wave equation
• Some trigonometrical inequalities with applications to the theory of series
• A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods
• A mixed finite element formulation for the boundary controllability of the wave equation
• Uniform stabilization of a viscous numerical approximation for a locally damped wave equation
• Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
• Geometrical aspects of exact boundary controllability for the wave equation - a numerical study
• Boundary observability for the space semi-discretizations of the 1 – d wave equation
• Dispersion-corrected explicit integration of the wave equation