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Volumn 43, Issue 4, 2005, Pages 1536-1571

Convergence of the Lagrange-Galerkin method for the equations modelling the motion of a fluid-rigid system

Author keywords

Finite element method; Fluid structure interaction; Incompressible Navier Stokes equations; Lagrange Galerkin method

Indexed keywords

DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; FLUID MECHANICS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 33747179201     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903438161     Document Type: Article
Times cited : (17)

References (29)
  • 1
    • 0003597268 scopus 로고
    • Springer-Verlag, Berlin, Translated from the third Russian edition by Roger Cooke
    • V.I. ARNOLD, Ordinary Differential Equations, Springer-Verlag, Berlin, 1992. Translated from the third Russian edition by Roger Cooke.
    • (1992) Ordinary Differential Equations
    • Arnold, V.I.1
  • 2
    • 0003210742 scopus 로고
    • The mathematical theory of finite element methods
    • Springer-Verlag, New York
    • S.C. BRENNER AND L.R. SCOTT, The Mathematical Theory of Finite Element Methods, Texts Appl. Math. 15, Springer-Verlag, New York, 1994.
    • (1994) Texts Appl. Math. , vol.15
    • Brenner, S.C.1    Scott, L.R.2
  • 4
    • 0003204969 scopus 로고
    • The finite element method for elliptic problems
    • North-Holland, Amsterdam
    • P.-G. CIARLET, The Finite Element Method for Elliptic Problems, Stud. Math. Appl. 4, North-Holland, Amsterdam, 1978.
    • (1978) Stud. Math. Appl. , vol.4
    • Ciarlet, P.-G.1
  • 5
    • 0034354912 scopus 로고    scopus 로고
    • Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid
    • C. CONCA, H.J. SAN MARTÍN, AND M. TUCSNAK, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations, 25 (2000), pp. 1019-1042.
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 1019-1042
    • Conca, C.1    San Martín, H.J.2    Tucsnak, M.3
  • 6
    • 0034355083 scopus 로고    scopus 로고
    • On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models
    • B. DESJARDINS AND M.J. ESTEBAN, On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models, Comm. Partial Differential Equations, 25 (2000), pp. 1399-1413.
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 1399-1413
    • Desjardins, B.1    Esteban, M.J.2
  • 7
    • 0003439976 scopus 로고
    • Princeton University Press, Princeton, NJ
    • L.P. EISENHART, Riemannian Geometry, Princeton University Press, Princeton, NJ, 1949.
    • (1949) Riemannian Geometry
    • Eisenhart, L.P.1
  • 8
    • 0035842860 scopus 로고    scopus 로고
    • The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids
    • C. FARHAT, P. GEUZAINE, AND C. GRANDMONT, The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids, J. Comput. Phys., 174 (2001), pp. 669-694.
    • (2001) J. Comput. Phys. , vol.174 , pp. 669-694
    • Farhat, C.1    Geuzaine, P.2    Grandmont, C.3
  • 9
    • 0032650723 scopus 로고    scopus 로고
    • A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements
    • L. FORMAGGIA AND F. NOBILE, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Numer. Math., 7 (1999), pp. 105-131.
    • (1999) East-West J. Numer. Math. , vol.7 , pp. 105-131
    • Formaggia, L.1    Nobile, F.2
  • 10
    • 0000197728 scopus 로고
    • On existence of weak solutions of the Navier-Stokes equations in regions with moving boundaries
    • H. FUJITA AND N. SAUER, On existence of weak solutions of the Navier-Stokes equations in regions with moving boundaries, J. Fac. Sci. Univ. Tokyo Sect. I, 17 (1970), pp. 403-420.
    • (1970) J. Fac. Sci. Univ. Tokyo Sect. I , vol.17 , pp. 403-420
    • Fujita, H.1    Sauer, N.2
  • 11
    • 0034930744 scopus 로고    scopus 로고
    • A priori error estimates for the arbitrary Lagrangian Eulerian formulation with finite elements
    • L. GASTALDI, A priori error estimates for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Numer. Math., 9 (2001), pp. 123-156.
    • (2001) East-west J. Numer. Math. , vol.9 , pp. 123-156
    • Gastaldi, L.1
  • 12
    • 0003197516 scopus 로고
    • Finite element approximation of the Navier-Stokes equations
    • Springer-Verlag, Berlin, New York
    • V. GIRAULT AND P.-A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Math. 749, Springer-Verlag, Berlin, New York, 1979.
    • (1979) Lecture Notes in Math. , vol.749
    • Girault, V.1    Raviart, P.-A.2
  • 13
    • 0034646896 scopus 로고    scopus 로고
    • A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow
    • R. GLOWINSKI, T.-W. PAN, T.I. HESLA, D.D. JOSEPH, AND J. PÉRIAUX, A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow, Comput. Methods Appl. Mech. Engrg., 184 (2000), pp. 241-267.
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.184 , pp. 241-267
    • Glowinski, R.1    Pan, T.-W.2    Hesla, T.I.3    Joseph, D.D.4    Périaux, J.5
  • 14
    • 0001105507 scopus 로고    scopus 로고
    • A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow
    • R. GLOWINSKI, T.-W. PAN, T.I. HESLA, D.D. JOSEPH, AND J. PÉRIAUX, A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys., 169 (2001), pp. 363-426.
    • (2001) J. Comput. Phys. , vol.169 , pp. 363-426
    • Glowinski, R.1    Pan, T.-W.2    Hesla, T.I.3    Joseph, D.D.4    Périaux, J.5
  • 15
    • 0035638389 scopus 로고    scopus 로고
    • Numerical analysis of some decoupling techniques for the approximation of the unsteady fluid structure interaction
    • C. GRANDMONT, V. GUIMET, AND Y. MADAY, Numerical analysis of some decoupling techniques for the approximation of the unsteady fluid structure interaction, Math. Models Methods Appl. Sci., 11 (2001), pp. 1349-1377.
    • (2001) Math. Models Methods Appl. Sci. , vol.11 , pp. 1349-1377
    • Grandmont, C.1    Guimet, V.2    Maday, Y.3
  • 16
    • 0034410608 scopus 로고    scopus 로고
    • Existence for an unsteady fluid-structure interaction problem
    • C. GRANDMONT AND Y. MADAY, Existence for an unsteady fluid-structure interaction problem, M2AN Math. Model. Numer. Anal., 34 (2000), pp. 609-636.
    • (2000) M2AN Math. Model. Numer. Anal. , vol.34 , pp. 609-636
    • Grandmont, C.1    Maday, Y.2
  • 17
    • 0001236805 scopus 로고    scopus 로고
    • Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions
    • M.D. GUNZBURGER, H.-C. LEE, AND G.A. SEREGIN, Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions, J. Math. Fluid Mech., 2 (2000), pp. 219-266.
    • (2000) J. Math. Fluid Mech. , vol.2 , pp. 219-266
    • Gunzburger, M.D.1    Lee, H.-C.2    Seregin, G.A.3
  • 18
    • 0038786628 scopus 로고
    • On existence of solutions of the Navier-Stokes equation in a time dependent domain
    • A. INOUE AND M. WAKIMOTO, On existence of solutions of the Navier-Stokes equation in a time dependent domain, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 24 (1977), pp. 303-319.
    • (1977) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.24 , pp. 303-319
    • Inoue, A.1    Wakimoto, M.2
  • 20
    • 0002823628 scopus 로고    scopus 로고
    • Direct simulations of 2D fluid-particle flows in biperiodic domains
    • B. MAURY, Direct simulations of 2D fluid-particle flows in biperiodic domains, J. Comput. Phys., 156 (1999), pp. 325-351.
    • (1999) J. Comput. Phys. , vol.156 , pp. 325-351
    • Maury, B.1
  • 23
    • 0001338807 scopus 로고
    • On the transport-diffusion algorithm and its applications to the Navier-Stokes equations
    • O. PIRONNEAU, On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numer. Math., 38 (1982), pp. 309-332.
    • (1982) Numer. Math. , vol.38 , pp. 309-332
    • Pironneau, O.1
  • 24
    • 0003208019 scopus 로고
    • Numerical approximation of partial differential equations
    • Springer-Verlag, Berlin
    • A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer Ser. Comput. Math. 23, Springer-Verlag, Berlin, 1994.
    • (1994) Springer Ser. Comput. Math. , vol.23
    • Quarteroni, A.1    Valli, A.2
  • 25
    • 0036488716 scopus 로고    scopus 로고
    • Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid
    • J.A. SAN MARTÍN, V. STAROVOITOV, AND M. TUCSNAK, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Ration. Mech. Anal., 161 (2002), pp. 113-147.
    • (2002) Arch. Ration. Mech. Anal. , vol.161 , pp. 113-147
    • San Martín, J.A.1    Starovoitov, V.2    Tucsnak, M.3
  • 26
    • 0001515792 scopus 로고
    • Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
    • E. SÜLI, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations, Numer. Math., 53 (1988), pp. 459-483.
    • (1988) Numer. Math. , vol.53 , pp. 459-483
    • Süli, E.1
  • 27
    • 15744401862 scopus 로고    scopus 로고
    • Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain
    • T. TAKAHASHI, Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, Adv. Differential Equations, 8 (2003), pp. 1499-1532.
    • (2003) Adv. Differential Equations , vol.8 , pp. 1499-1532
    • Takahashi, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.