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Boundary observability of a numerical approximation scheme of Maxwell's system in a cube

  • Autores: Serge Nicaise
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 1, 2008, págs. 27-52
  • Idioma: inglés
  • DOI: 10.1007/bf03191180
  • Enlaces
  • Referencias bibliográficas
    • C. Castro and S. Micu, Boundary controllability of a linear semidiscrete 1-D wave equation derived from a mixed finite element method, Numer....
    • C. Castro, S. Micu, and A. Münch, Numerical approximation of the boundary control of the 2-D wave equation with mixed finite elements, IMA...
    • M. Costabel, M. Dauge, and S. Nicaise, Singularities of Maxwell interface problems, M2AN Math. Model. Numer. Anal. 33 (1999), 627–649.
    • M.M. Eller and J.E. Masters, Exact boundary controllability of electromagnetic fields in a general region, Appl. Math. Optim. 45 (2002), 99–123.
    • R. Glowinski, Ensuring well-posedness by analogy: Stokes problem and boundary control of the wave equation, J. Comput. Phys. 103 (1992), 189–221.
    • R. Glowinski, W. Kinton, and M.F. Wheeler, A mixed finite element formulation for the boundary controllability of the wave equation, Internat....
    • R. Glowinski, C.H. Li, and J.L. Lions, A numerical approach to the exact boundary controllability of the wave equation I, Dirichlet controls:...
    • R. Glowinski and J.L. Lions, Exact and approximate controllability for distributed parameter systems, Acta Numerica (1996), 159–333.
    • L.F. Ho, Observabilité frontière de l’équation des ondes (Boundary observability of the wave equation), C. R. Acad. Sci. Paris Sér. I Math....
    • J.A. Infante and E. Zuazua, Boundary observability for the space semidiscretizations of the 1-D wave equation, M2AN Math. Model. Numer. Anal....
    • E. Isaacson and H.B. Keller, Analysis of Numerical Methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966.
    • B.V. Kapitanov, Stabilization and exact boundary controllability for Maxwell’s equations, SIAM J. Control Optim. 32 (1994), 408–420.
    • K.A. Kime, Boundary exact controllability of Maxwell’s equations in a spherical region, SIAM J. Control Optim. 28 (1990), 294–319.
    • V. Komornik, Boundary stabilization, observation and control of Maxwell’s equations, Panamer. Math. J. 4 (1994), 47–61.
    • V. Komornik, Exact Controllability and Stabilization, The Multiplier Method, Research in Applied Mathematics, Masson, Paris, 1994.
    • J.E. Lagnese, Exact controllability of Maxwell’s equations in a general region, SIAM J. Control Optim. 27 (1989), 374–388.
    • L. León and E. Zuazua, Boundary controllability of the finite-difference space semidiscretizations of the beam equation, (Special volume in...
    • J.L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués I, Recherches en Mathématiques Appliquées 8, Masson,...
    • P. Monk, A mixed method for approximating Maxwell’s equations, SIAM J. Numer. Anal. 28 (1991), 1610–1634.
    • P. Monk, Finite Element Methods for Maxwell’s Equations, Numerical Mathematics and Scientific Computation, Oxford University Press, New York,...
    • P. Monk and E. Süli, A convergence analysis of Yee’s scheme on nonuniform grids, SIAM J. Numer. Anal. 31 (1994), 393–412.
    • A. Münch, A uniformly controllable and implicit scheme for the 1-D wave equation, M2AN Math. Model. Numer. Anal. 39 (2005), 377–418.
    • M. Negreanu and E. Zuazua, Uniform boundary controllability of a discrete 1-D wave equation, Systems Control Lett. 48 (2003), 261–280.
    • M. Negreanu and E. Zuazua, Discrete Ingham inequalities and applications, SIAM J. Numer. Anal. 44 (2006), 412–448.
    • S. Nicaise, Exact boundary controllability of Maxwell’s equations in heterogeneous media and an application to an inverse source problem,...
    • S. Nicaise and C. Pignotti, Boundary stabilization of Maxwell’s equations with space-time variable coefficients, ESAIM Control Optim. Calc....
    • S. Nicaise and C. Pignotti, Energy decay rates for solutions of Maxwell’s system with a memory boundary condition, Collect. Math., to appear.
    • K.D. Phung, Contrôle et stabilisation d’ondes électromagnétiques, ESAIM Control Optim. Calc. Var. 5 (2000), 87–137.
    • C. Pignotti, Observability and controllability of Maxwell’s equations, Rend. Mat. Appl. (7) 19 (1999), 523–546.
    • K. Ramdani, T. Takahashi, and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations: application...
    • D.L. Russell, The Dirichlet-Neumann boundary control problem associated with Maxwell’s equations in a cylindrical region, SIAM J. Control...
    • L.R.T. Tébou and E. Zuazua, Uniform exponential long time decay for the space semidiscretization of a locally damped wave equation via an...
    • N. Weck, Exact boundary controllability of a Maxwell problem, SIAM J. Control Optim. 38 (2000), 736–750.
    • K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propagation...
    • X. Zhang, Exact internal controllability of Maxwell’s equations, Appl. Math. Optim. 41 (2000), 155–170.
    • Q. Zhou, Exact internal controllability of Maxwell’s equations, Japan J. Indust. Appl. Math. 14 (1997), 245–256.
    • E. Zuazua, Boundary observability for the finite-difference space semidiscretizations of the 2-D wave equation in the square, J. Math. Pures...
    • E. Zuazua, Optimal and approximate control of finite-difference approximation schemes for the 1-D wave equation, Rend. Mat. Appl. (7) 24 (2004),...
    • E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods, SIAM Rev. 47 (2005), 197–243.

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