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Volumn 39, Issue 3, 2007, Pages 211-222

Mathematical foundations of the immersed finite element method

Author keywords

Euler Lagrange mapping; Fluid Structure interaction; Immersed finite element method

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; CONFORMAL MAPPING; FINITE ELEMENT METHOD; NUMERICAL METHODS;

EID: 37849186435     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-005-0018-5     Document Type: Article
Times cited : (100)

References (36)
  • 1
    • 0000443756 scopus 로고
    • Error-bounds for finite element method
    • Babuska I (1971) Error-bounds for finite element method. Numer Math 16:322-333
    • (1971) Numer Math , vol.16 , pp. 322-333
    • Babuska, I.1
  • 2
    • 2342565951 scopus 로고    scopus 로고
    • Finite element developments for general fluid flows with structural interactions
    • Bathe KJ, Zhang H (2004) Finite element developments for general fluid flows with structural interactions. Int J Numer Meth Eng 60(1):213-232
    • (2004) Int J Numer Meth Eng , vol.60 , Issue.1 , pp. 213-232
    • Bathe, K.J.1    Zhang, H.2
  • 4
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers
    • Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal Numer R-2:129-151
    • (1974) RAIRO Anal Numer R-2 , pp. 129-151
    • Brezzi, F.1
  • 5
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp Methods Appl Mech Eng 32:199-259
    • (1982) Comp Methods Appl Mech Eng , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 7
    • 30944458239 scopus 로고    scopus 로고
    • Angioplasty stent modeling using Immersed Finite Element Method
    • submitted
    • Gay M, Zhang L, Liu WK (2005) Angioplasty stent modeling using Immersed Finite Element Method. Comput Methods Appl Mech Eng (submitted)
    • (2005) Comput Methods Appl Mech Eng
    • Gay, M.1    Zhang, L.2    Liu, W.K.3
  • 8
    • 0000347507 scopus 로고    scopus 로고
    • Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique
    • Hu HH, Patankar NA, Zhu MY (2001) Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J Comput Phys 169:427-462
    • (2001) J Comput Phys , vol.169 , pp. 427-462
    • Hu, H.H.1    Patankar, N.A.2    Zhu, M.Y.3
  • 9
    • 0024067463 scopus 로고
    • Viscous flow with large free surface motion
    • Huerta A, Liu WK (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69:277-324
    • (1988) Comput Methods Appl Mech Eng , vol.69 , pp. 277-324
    • Huerta, A.1    Liu, W.K.2
  • 10
    • 0022810283 scopus 로고
    • A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
    • Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59:85-99
    • (1986) Comput Methods Appl Mech Eng , vol.59 , pp. 85-99
    • Hughes, T.J.R.1    Franca, L.P.2    Balestra, M.3
  • 11
    • 0019718251 scopus 로고
    • Lagrangian-Eulerian finite element formulations for incompressible viscous flows
    • Hughes TJR, Liu WK, Zimmerman TK (1981) Lagrangian-Eulerian finite element formulations for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329-349
    • (1981) Comput Methods Appl Mech Eng , vol.29 , pp. 329-349
    • Hughes, T.J.R.1    Liu, W.K.2    Zimmerman, T.K.3
  • 12
    • 0032666655 scopus 로고    scopus 로고
    • Advanced mesh generation and update methods for 3d flow simulations
    • Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3d flow simulations. Comput Mech 23: 130-143
    • (1999) Comput Mech , vol.23 , pp. 130-143
    • Johnson, A.A.1    Tezduyar, T.E.2
  • 13
    • 0000868581 scopus 로고    scopus 로고
    • An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
    • Lai MC, Peskin CS (2000) An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J Comput Phys 160:705-719
    • (2000) J Comput Phys , vol.160 , pp. 705-719
    • Lai, M.C.1    Peskin, C.S.2
  • 14
    • 37949056856 scopus 로고    scopus 로고
    • Meshfree Particle Methods: Chapt. 8. Springer, Berlin Heidelberg New York
    • Li S, Liu WK (2004) Meshfree Particle Methods: Chapt. 8. Springer, Berlin Heidelberg New York
    • (2004)
    • Li, S.1    Liu, W.K.2
  • 15
    • 0019573324 scopus 로고
    • Finite element procedures for fluid-structure interactions and application to liquid storage tanks
    • Liu WK (1981) Finite element procedures for fluid-structure interactions and application to liquid storage tanks. Nucl Eng Des 65:221-238
    • (1981) Nucl Eng des , vol.65 , pp. 221-238
    • Liu, W.K.1
  • 16
    • 0022789785 scopus 로고
    • Fluid-structure interaction of tanks with an eccentric core barrel
    • Liu WK, Gvildys J (1986) Fluid-structure interaction of tanks with an eccentric core barrel. Comput Methods Appl Mech Eng 58:51-77
    • (1986) Comput Methods Appl Mech Eng , vol.58 , pp. 51-77
    • Liu, W.K.1    Gvildys, J.2
  • 18
    • 0020163157 scopus 로고
    • Computer implementation aspects for fluid-structure interaction problems
    • Liu WK, Ma DC (1982) Computer implementation aspects for fluid-structure interaction problems. Comput Methods Appl Mech Eng 31:129-148
    • (1982) Comput Methods Appl Mech Eng , vol.31 , pp. 129-148
    • Liu, W.K.1    Ma, D.C.2
  • 21
    • 11244275011 scopus 로고    scopus 로고
    • Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics
    • Liu Y, Zhang L, Wang X, Liu WK (2004) Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics. Int J Numer Methods Fluids 46:1237-1252
    • (2004) Int J Numer Methods Fluids , vol.46 , pp. 1237-1252
    • Liu, Y.1    Zhang, L.2    Wang, X.3    Liu, W.K.4
  • 22
    • 0031371610 scopus 로고    scopus 로고
    • Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating mammalian heart
    • McQueen DM, Peskin CS (1997) Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating mammalian heart. J Supercomput 11:213-236
    • (1997) J Supercomput , vol.11 , pp. 213-236
    • McQueen, D.M.1    Peskin, C.S.2
  • 23
    • 0017424014 scopus 로고
    • Numerical analysis of blood flow in the heart
    • Peskin CS (1977) Numerical analysis of blood flow in the heart. J Comput Phys 25:220-252
    • (1977) J Comput Phys , vol.25 , pp. 220-252
    • Peskin, C.S.1
  • 24
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • Peskin CS (2002) The immersed boundary method. Acta Numerica 11:479-517
    • (2002) Acta Numerica , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 25
    • 45149143078 scopus 로고
    • A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid
    • Peskin CS, McQueen DM (1989) A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. J Comput Phys 81(2): 372-405
    • (1989) J Comput Phys , vol.81 , Issue.2 , pp. 372-405
    • Peskin, C.S.1    McQueen, D.M.2
  • 28
    • 77956849889 scopus 로고
    • Stabilized finite element formulations for incompressible-flow computations
    • Tezduyar TE (1992) Stabilized finite element formulations for incompressible-flow computations. Adv Appl Mech 28:1-44
    • (1992) Adv Appl Mech , vol.28 , pp. 1-44
    • Tezduyar, T.E.1
  • 30
    • 2042465004 scopus 로고    scopus 로고
    • Enhanced-Discretization Space-Time Technique (EDSTT)
    • Tezduyar TE, Sathe S (2004) Enhanced-Discretization Space-Time Technique (EDSTT). Comput Methods Appl Mech Eng 193:1385-1401
    • (2004) Comput Methods Appl Mech Eng , vol.193 , pp. 1385-1401
    • Tezduyar, T.E.1    Sathe, S.2
  • 31
    • 0035599464 scopus 로고    scopus 로고
    • Finite element methods for flow problems with moving boundaries and interfaces
    • Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Archives Comput Methods Eng 8(2):83-130
    • (2001) Archives Comput Methods Eng , vol.8 , Issue.2 , pp. 83-130
    • Tezduyar, T.E.1
  • 32
    • 0000714458 scopus 로고
    • Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods
    • Tu C, Peskin CS (1992) Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods. SIAM J Sci Stat Comput 13(6): 1361-1376
    • (1992) SIAM J Sci Stat Comput , vol.13 , Issue.6 , pp. 1361-1376
    • Tu, C.1    Peskin, C.S.2
  • 33
    • 0037423944 scopus 로고    scopus 로고
    • Particulate flow simulations using lubrication theory solution enrichment
    • Wagner GJ, Ghosal S, Liu WK (2003) Particulate flow simulations using lubrication theory solution enrichment. Int J Numer Methods Eng 56:1261-1289
    • (2003) Int J Numer Methods Eng , vol.56 , pp. 1261-1289
    • Wagner, G.J.1    Ghosal, S.2    Liu, W.K.3
  • 34
    • 0035972924 scopus 로고    scopus 로고
    • The extended finite element method for rigid particles in stokes flow
    • Wagner GJ, Moës N, Liu WK, Belytschko T (2001) The extended finite element method for rigid particles in stokes flow. Int J Numer 51:293-313
    • (2001) Int J Numer , vol.51 , pp. 293-313
    • Wagner, G.J.1    Moës, N.2    Liu, W.K.3    Belytschko, T.4
  • 35
    • 1842418427 scopus 로고    scopus 로고
    • Extended immersed boundary method using FEM and RKPM
    • Wang X, Liu WK (2004) Extended immersed boundary method using FEM and RKPM. Comput Methods Appl Mech Eng 193(12-14): 1305-1321
    • (2004) Comput Methods Appl Mech Eng , vol.193 , Issue.12-14 , pp. 1305-1321
    • Wang, X.1    Liu, W.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.