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Volumn 28, Issue 1, 2008, Pages 186-214

Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square

Author keywords

Exact controllability; Numerical approximation of controls; Observability; Wave equation

Indexed keywords

OBSERVABILITY; WAVE EQUATIONS;

EID: 37849044935     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drm012     Document Type: Article
Times cited : (41)

References (14)
  • 1
    • 0001835676 scopus 로고
    • Exponentially stable approximations of weakly damped wave equations
    • Estimation and Control of Distributed Parameter Systems Vorau, 1990, W. Desch, F. Kappel & K. Kunisch eds, Basel: Birkhäuser, pp
    • BANKS, H. T., ITO, K. & WANG, C. (1991) Exponentially stable approximations of weakly damped wave equations. Estimation and Control of Distributed Parameter Systems (Vorau, 1990) (W. Desch, F. Kappel & K. Kunisch eds). International Series of Numerical Mathematics, vol.100. Basel: Birkhäuser, pp. 1-33.
    • (1991) International Series of Numerical Mathematics , vol.100 , pp. 1-33
    • BANKS, H.T.1    ITO, K.2    WANG, C.3
  • 2
    • 0002145565 scopus 로고
    • On the general theory of exact controllability for skew symmetric operators
    • BENSOUSSAN, A. (1990) On the general theory of exact controllability for skew symmetric operators. Acta Appl. Math., 20, 197-229.
    • (1990) Acta Appl. Math , vol.20 , pp. 197-229
    • BENSOUSSAN, A.1
  • 3
    • 19644373170 scopus 로고    scopus 로고
    • Higher-Order Numerical Methods for Transient Wave Equations
    • Berlin, Germany: Springer
    • COHEN, G. C. (2002) Higher-Order Numerical Methods for Transient Wave Equations. Scientific Computation. Berlin, Germany: Springer.
    • (2002) Scientific Computation
    • COHEN, G.C.1
  • 4
    • 0002717380 scopus 로고
    • Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation
    • GLOWINSKI, R. (1991) Ensuring well-posedness by analogy; Stokes problem and boundary control for the wave equation. J. Comput. Phys., 103, 189-221.
    • (1991) J. Comput. Phys , vol.103 , pp. 189-221
    • GLOWINSKI, R.1
  • 5
    • 0024884091 scopus 로고    scopus 로고
    • GLOWINSKI, R., KINTON, W. & WHEELER, M. F. (1989) A. mixed finite element formulation for the boundar controllability of the wave equation. Int. J. Numer. Methods Eng., 27, 623-636.
    • GLOWINSKI, R., KINTON, W. & WHEELER, M. F. (1989) A. mixed finite element formulation for the boundar controllability of the wave equation. Int. J. Numer. Methods Eng., 27, 623-636.
  • 6
    • 77951516889 scopus 로고    scopus 로고
    • GLOWINSKI, R., LI, C. & LIONS, J.-L. (1990) A. numerical approach to the exact boundary controllability of the wave equation (I). Dirichlet controls: description of the numerical methods. Jpn. J. Appl. Math., 7, 1-76.
    • GLOWINSKI, R., LI, C. & LIONS, J.-L. (1990) A. numerical approach to the exact boundary controllability of the wave equation (I). Dirichlet controls: description of the numerical methods. Jpn. J. Appl. Math., 7, 1-76.
  • 7
    • 84959656664 scopus 로고    scopus 로고
    • Exact and approximate controllability for distributed parameter systems
    • GLOWINSKI, R. & LIONS, J.-L. (1996) Exact and approximate controllability for distributed parameter systems. Acta Numer., 5, 159-333.
    • (1996) Acta Numer , vol.5 , pp. 159-333
    • GLOWINSKI, R.1    LIONS, J.-L.2
  • 8
    • 0033411395 scopus 로고    scopus 로고
    • Boundary observability for the space semi-discretization of the 1-D wave equation
    • INFANTE, J. A. & ZUAZUA, E. (1999) Boundary observability for the space semi-discretization of the 1-D wave equation. Math Model Numer. Anal., 33, 407-438.
    • (1999) Math Model Numer. Anal , vol.33 , pp. 407-438
    • INFANTE, J.A.1    ZUAZUA, E.2
  • 9
    • 0032358487 scopus 로고    scopus 로고
    • The Trotter-Kato theorem and approximations of PDE's
    • KAPPEL, F. & ITO, K. (1998) The Trotter-Kato theorem and approximations of PDE's. Math Comput., 67, 21-44.
    • (1998) Math Comput , vol.67 , pp. 21-44
    • KAPPEL, F.1    ITO, K.2
  • 11
    • 70350630547 scopus 로고
    • Mixed and hybrid methods
    • P. G. Ciarlet & J.-L. Lions eds, Amsterdam, The Netherlands: North-Holland, pp
    • ROBERTS, J. E. & THOMAS, J.-M. (1989) Mixed and hybrid methods. Handbook of Numerical Analysis (P. G. Ciarlet & J.-L. Lions eds), vol. 2. Amsterdam, The Netherlands: North-Holland, pp. 523-639.
    • (1989) Handbook of Numerical Analysis , vol.2 , pp. 523-639
    • ROBERTS, J.E.1    THOMAS, J.-M.2
  • 12
    • 0000125555 scopus 로고
    • Group velocity in finite difference schemes
    • TREFETHEN, L. N. (1982) Group velocity in finite difference schemes. SIAM Rev., 24, 113-136.
    • (1982) SIAM Rev , vol.24 , pp. 113-136
    • TREFETHEN, L.N.1
  • 13
    • 0033542257 scopus 로고    scopus 로고
    • Boundary observability for the finite difference space semi-discretizations of the 2-D wave equation in the square
    • ZUAZUA, E. (1999) Boundary observability for the finite difference space semi-discretizations of the 2-D wave equation in the square. J. Math Pures Appl., 78, 523-563.
    • (1999) J. Math Pures Appl , vol.78 , pp. 523-563
    • ZUAZUA, E.1
  • 14
    • 21244472382 scopus 로고    scopus 로고
    • Propagation, observation, control and numerical approximation of waves
    • ZUAZUA, E. (2005) Propagation, observation, control and numerical approximation of waves. SIAM Rev., 47, 197-243.
    • (2005) SIAM Rev , vol.47 , pp. 197-243
    • ZUAZUA, E.1


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