메뉴 건너뛰기




Volumn 196, Issue 41-44, 2007, Pages 4045-4058

Interior penalty variational multiscale method for the incompressible Navier-Stokes equation: Monitoring artificial dissipation

Author keywords

A posteriori error estimation; Energy balance; Incompressible flow; Interior penalty; Navier Stokes equations; Numerical dissipation; Stabilized finite element methods; Variational multiscale methods

Indexed keywords

ENERGY BALANCE; ENERGY DISSIPATION; ERROR ANALYSIS; FINITE ELEMENT METHOD; HEURISTIC METHODS; NAVIER STOKES EQUATIONS; POWER SPECTRUM; REYNOLDS NUMBER; VARIATIONAL TECHNIQUES;

EID: 34547599621     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.03.025     Document Type: Article
Times cited : (35)

References (44)
  • 1
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 4 (1982) 742-760
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.4 , pp. 742-760
    • Arnold, D.N.1
  • 2
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 5 (2001/2002) 1749-1779
    • (2001) SIAM J. Numer. Anal. , vol.39 , Issue.5 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 3
    • 34547584617 scopus 로고    scopus 로고
    • Y. Bazilevs, T.J.R Hughes, Weak imposition of dirichlet boundary conditions in fluid mechanics, Technical Report ICES 05-25, The Institute For Computational Engineering and Sciences, University of Texas, 2005.
  • 4
    • 0036740009 scopus 로고    scopus 로고
    • Mesh adaptation for Dirichlet flow control via Nitsche's method
    • Becker R. Mesh adaptation for Dirichlet flow control via Nitsche's method. Comm. Numer. Methods Engrg. 18 9 (2002) 669-680
    • (2002) Comm. Numer. Methods Engrg. , vol.18 , Issue.9 , pp. 669-680
    • Becker, R.1
  • 5
    • 0001167160 scopus 로고    scopus 로고
    • A finite element pressure gradient stabilization for the Stokes equations based on local projections
    • Becker R., and Braack M. A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38 4 (2001) 173-199
    • (2001) Calcolo , vol.38 , Issue.4 , pp. 173-199
    • Becker, R.1    Braack, M.2
  • 6
    • 33745302770 scopus 로고    scopus 로고
    • Estimates for the L 2-projection onto continuous finite element spaces in a weighted Lp-norm
    • Boman M. Estimates for the L 2-projection onto continuous finite element spaces in a weighted Lp-norm. BIT 46 2 (2006) 249-260
    • (2006) BIT , vol.46 , Issue.2 , pp. 249-260
    • Boman, M.1
  • 7
    • 33751034242 scopus 로고    scopus 로고
    • Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method
    • Braack M., and Burman E. Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. SIAM J. Numer. Anal. 43 6 (2006) 2544-2566
    • (2006) SIAM J. Numer. Anal. , vol.43 , Issue.6 , pp. 2544-2566
    • Braack, M.1    Burman, E.2
  • 8
    • 0001078341 scopus 로고
    • Choosing bubbles for advection-diffusion problems
    • Brezzi F., and Russo A. Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4 4 (1994) 571-587
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , Issue.4 , pp. 571-587
    • Brezzi, F.1    Russo, A.2
  • 9
    • 0034310567 scopus 로고    scopus 로고
    • Adaptive finite element methods for compressible flow
    • Burman E. Adaptive finite element methods for compressible flow. Comput. Methods Appl. Mech. Engrg. 190 8-10 (2000) 1137-1162
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , Issue.8-10 , pp. 1137-1162
    • Burman, E.1
  • 10
    • 34547602459 scopus 로고    scopus 로고
    • E. Burman, An interior penalty variational multiscale method for high reynolds number flows, Technical Report 18, EPFL/IACS, 2005.
  • 11
    • 33745674971 scopus 로고    scopus 로고
    • A unified analysis for conforming and non-conforming stabilized finite element methods using interior penalty
    • Burman E. A unified analysis for conforming and non-conforming stabilized finite element methods using interior penalty. SIAM J. Numer. Anal. 43 5 (2005) 2012-2033
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.5 , pp. 2012-2033
    • Burman, E.1
  • 12
    • 34547582408 scopus 로고    scopus 로고
    • An interior penalty variational multiscale method for high Reynolds number flows
    • Springer Verlag
    • Burman E. An interior penalty variational multiscale method for high Reynolds number flows. Numerical Mathematics and Advanced Applications, Enumath 2005 (2006), Springer Verlag
    • (2006) Numerical Mathematics and Advanced Applications, Enumath 2005
    • Burman, E.1
  • 13
    • 34547607660 scopus 로고    scopus 로고
    • Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations
    • Burman E., and Ern A. Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comp. 76 (2007) 1119-1140
    • (2007) Math. Comp. , vol.76 , pp. 1119-1140
    • Burman, E.1    Ern, A.2
  • 14
    • 34547273293 scopus 로고    scopus 로고
    • Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
    • Burman E., and Fernàndez M. Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence. Numer. Math. (2007)
    • (2007) Numer. Math.
    • Burman, E.1    Fernàndez, M.2
  • 15
    • 33751063232 scopus 로고    scopus 로고
    • Continuous interior penalty finite element method for Oseen's equations
    • Burman E., Fernández M.A., and Hansbo P. Continuous interior penalty finite element method for Oseen's equations. SIAM J. Numer. Anal. 44 3 (2006) 1248-1274
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.3 , pp. 1248-1274
    • Burman, E.1    Fernández, M.A.2    Hansbo, P.3
  • 16
    • 84893445106 scopus 로고    scopus 로고
    • E. Burman, M.A. Fernández, P. Hansbo, Edge stabilization: an interior penalty method for the incompressible Navier-Stokes equation, in: Proceedings of the Fourth European Congress on Computational Methods in Applied Sciences and Engineering, vol. I, 2004.
  • 17
    • 2042428741 scopus 로고    scopus 로고
    • Edge stabilization for Galerkin approximations of convection-diffusion problems
    • Burman E., and Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1437-2453
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 1437-2453
    • Burman, E.1    Hansbo, P.2
  • 18
    • 33645071596 scopus 로고    scopus 로고
    • A stabilized non-conforming finite element method for incompressible flow
    • Burman E., and Hansbo P. A stabilized non-conforming finite element method for incompressible flow. Comput. Methods Appl. Mech. Engrg. 195 23-24 (2006) 2881-2899
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , Issue.23-24 , pp. 2881-2899
    • Burman, E.1    Hansbo, P.2
  • 19
    • 0037200448 scopus 로고    scopus 로고
    • Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
    • Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Engrg. 191 39-40 (2002) 4295-4321
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , Issue.39-40 , pp. 4295-4321
    • Codina, R.1
  • 20
    • 34547564964 scopus 로고    scopus 로고
    • S. Collis, The DG/VMS method for unified turbulence simulation, Technical report, AIAA paper 2002-3124, 2002.
  • 21
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Computing methods in applied sciences (Second International Symposium, Versailles, 1975), Springer, Berlin
    • Douglas J., and Dupont T. Interior penalty procedures for elliptic and parabolic Galerkin methods. Computing methods in applied sciences (Second International Symposium, Versailles, 1975). Lecture Notes in Physics vol. 58 (1976), Springer, Berlin 207-216
    • (1976) Lecture Notes in Physics , vol.58 , pp. 207-216
    • Douglas, J.1    Dupont, T.2
  • 22
    • 1842483026 scopus 로고    scopus 로고
    • Approximating local averages of fluid velocities: The equilibrium Navier-Stokes equations
    • Dunca A., John V., and Layton W. Approximating local averages of fluid velocities: The equilibrium Navier-Stokes equations. Appl. Numer. Math. 49 2 (2004) 187-205
    • (2004) Appl. Numer. Math. , vol.49 , Issue.2 , pp. 187-205
    • Dunca, A.1    John, V.2    Layton, W.3
  • 23
    • 0009522795 scopus 로고
    • Introduction to adaptive methods for differential equations
    • Acta numerica 1995, Cambridge University Press, Cambridge
    • Eriksson K., Estep D., Hansbo P., and Johnson C. Introduction to adaptive methods for differential equations. Acta numerica 1995. Acta Numer (1995), Cambridge University Press, Cambridge 105-158
    • (1995) Acta Numer , pp. 105-158
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 24
    • 34547600978 scopus 로고    scopus 로고
    • J. Freund, R. Stenberg, On weakly imposed boundary conditions for second order problems. In: M. Morandi Cecchi et al., (Eds.), Proceedings of the Ninth International Conference on Finite Elements in Fluids, Venice, 1995, pp. 327-336.
  • 25
    • 23044435344 scopus 로고    scopus 로고
    • Large eddy simulation of turbulent incompressible flows by a three-level finite element method
    • Gravemeier V., Wall W.A., and Ramm E. Large eddy simulation of turbulent incompressible flows by a three-level finite element method. Int. J. Numer. Methods Fluids 48 10 (2005) 1067-1099
    • (2005) Int. J. Numer. Methods Fluids , vol.48 , Issue.10 , pp. 1067-1099
    • Gravemeier, V.1    Wall, W.A.2    Ramm, E.3
  • 26
    • 0025547284 scopus 로고
    • A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
    • Hansbo P., and Szepessy A. A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 84 2 (1990) 175-192
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.84 , Issue.2 , pp. 175-192
    • Hansbo, P.1    Szepessy, A.2
  • 29
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
    • Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput. Methods Appl. Mech. Engrg. 127 1-4 (1995) 387-401
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , Issue.1-4 , pp. 387-401
    • Hughes, T.J.R.1
  • 31
    • 0001769879 scopus 로고    scopus 로고
    • Large eddy simulation and the variational multiscale method
    • Hughes T.J.R., Mazzei L., and Jansen K.E. Large eddy simulation and the variational multiscale method. Comput. Vis. Sci. 3 (2000) 47-59
    • (2000) Comput. Vis. Sci. , vol.3 , pp. 47-59
    • Hughes, T.J.R.1    Mazzei, L.2    Jansen, K.E.3
  • 32
    • 25444487960 scopus 로고    scopus 로고
    • An assessment of two models for the subgrid scale tensor in the rational LES model
    • John V. An assessment of two models for the subgrid scale tensor in the rational LES model. J. Comput. Appl. Math. 173 1 (2005) 57-80
    • (2005) J. Comput. Appl. Math. , vol.173 , Issue.1 , pp. 57-80
    • John, V.1
  • 33
    • 34547596031 scopus 로고    scopus 로고
    • V. John, S. Kaya, Finite element error analysis and implementation of a variational multiscale method for the Navier-Stokes equations, Preprint University of Magdeburg, 2003.
  • 34
    • 0001255117 scopus 로고
    • Numerics and hydrodynamic stability: toward error control in computational fluid dynamics
    • Johnson C., Rannacher R., and Boman M. Numerics and hydrodynamic stability: toward error control in computational fluid dynamics. SIAM J. Numer. Anal. 32 4 (1995) 1058-1079
    • (1995) SIAM J. Numer. Anal. , vol.32 , Issue.4 , pp. 1058-1079
    • Johnson, C.1    Rannacher, R.2    Boman, M.3
  • 35
    • 30344470638 scopus 로고    scopus 로고
    • A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
    • Kaya S., and Rivière B. A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. 43 4 (2005) 1572-1595
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.4 , pp. 1572-1595
    • Kaya, S.1    Rivière, B.2
  • 36
    • 0001277608 scopus 로고
    • Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers
    • Kolmogorov A.N. Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30 299 (1941)
    • (1941) Dokl. Akad. Nauk SSSR , vol.30 , Issue.299
    • Kolmogorov, A.N.1
  • 37
    • 36849114603 scopus 로고
    • Inertial ranges in two-dimensional turbulence
    • Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (1967) 1417-1423
    • (1967) Phys. Fluids , vol.10 , pp. 1417-1423
    • Kraichnan, R.H.1
  • 38
    • 0033197176 scopus 로고    scopus 로고
    • Weak imposition of "no-slip" conditions in finite element methods
    • Layton W. Weak imposition of "no-slip" conditions in finite element methods. Comput. Math. Appl. 38 5-6 (1999) 129-142
    • (1999) Comput. Math. Appl. , vol.38 , Issue.5-6 , pp. 129-142
    • Layton, W.1
  • 39
    • 0037175406 scopus 로고    scopus 로고
    • A connection between subgrid scale eddy viscosity and mixed methods
    • Layton W. A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comput. 133 1 (2002) 147-157
    • (2002) Appl. Math. Comput. , vol.133 , Issue.1 , pp. 147-157
    • Layton, W.1
  • 40
    • 84971961701 scopus 로고
    • The mixing layer and its coherence examined from the point of view of two-dimensional turbulence
    • Lesieur M., Staquet C., Le Roy P., and Comte P. The mixing layer and its coherence examined from the point of view of two-dimensional turbulence. J. Fluid Mech. 192 (1988) 511-534
    • (1988) J. Fluid Mech. , vol.192 , pp. 511-534
    • Lesieur, M.1    Staquet, C.2    Le Roy, P.3    Comte, P.4
  • 41
    • 34547566106 scopus 로고    scopus 로고
    • J.-L. Lions, E. Magenes, Problèmes aux limites non-homogènes et applications. Travaux et Recherches Mathématiques, No. 17, vol. 1., Dunod, Paris, 1968.
  • 42
    • 84951671794 scopus 로고
    • Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
    • Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9-15
    • (1971) Abh. Math. Sem. Univ. Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.1
  • 43
    • 34547612375 scopus 로고    scopus 로고
    • A. Ouazzi, S. Turek, Unified edge-oriented stabilization of non-conforming finite element methods for incompressible flow problems, Technical Report 284, Universität Dortmund, 2005.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.