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1994 | 29 | 1 | 85-104
Tytuł artykułu

Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
85-104
Opis fizyczny
Daty
wydano
1994
Twórcy
autor
  • Mathematics Department, Magdeburg University of Technology, PF 4120, D-39016 Magdeburg, Germany
Bibliografia
  • [BF] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York 1991.
  • [DW] J. Douglas, Jr., and J. Wang, An absolutely stabilized finite element method for the Stokes problem, Math. Comp. 52 (186) (1989), 495-508.
  • [FD] L. P. Franca and E. G. Dutra do Carmo, The Galerkin-gradient-least-squares method, Comput. Methods Appl. Mech. Engrg. 74 (1989), 41-54.
  • [FFH] L. P. Franca, S. L. Frey and T. J. R. Hughes, Stabilized finite element methods: I. Applications to the advective-diffusive model, ibid., to appear.
  • [FS] L. P. Franca and R. Stenberg, Error analysis of some Galerkin-least-squares methods for the elasticity equations, SIAM J. Numer. Anal. (1991), to appear.
  • [GR] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer, 1986.
  • [HS] P. Hansbo and A. Szepessy, A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 84 (1990), 175-192.
  • [Hu] T. J. R. Hughes, Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations, Internat. J. Numer. Methods Fluids 7 (1987), 1261-1275.
  • [Ja] C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Studentlitteratur, Sweden, 1987.
  • [Jb] C. Johnson, Adaptive finite element methods for diffusive and convective problems, Comput. Methods Appl. Mech. Engrg. 82 (1990), 301-322.
  • [KR] R. Kornhuber and R. Roitzsch, On adaptive grid refinement in the presence of internal and boundary layers, IMPACT of Computing in Science and Engineering 2 (1990), 40-72.
  • [LA] G. Lube and A. Auge, Regularized mixed finite element approximations of incompressible flow problems. II. Navier-Stokes flow, preprint, TU Magdeburg, 1991.
  • [P] R. Pierre, Simple $C^0$ approximation for the computation of incompressible flow, Comput. Methods Appl. Mech. Engrg. 68 (1988), 205-227.
  • [T] R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conf. Ser. in Appl. Math. 41, SIAM, 1983.
  • [Tea] T. E. Tezduyar, R. Shih, S. Mittal and S. E. Ray, Incompressible flow computations with stabilized bilinear and linear equal-order interpolation velocity-pressure elements, preprint UMSI 90/165, Univ. of Minnesota, 1990.
  • [Teb] T. E. Tezduyar, Stabilized finite element formulations for incompressible flow computations, von Karman Institute for Fluid Dynamics, Lecture Series 1991-01.
  • [Wa] L. B. Wahlbin, Local behavior in finite element methods, in: Handbook of Numerical Analysis, P. G. Ciarlet and J. L. Lions (eds.), Vol. II, North-Holland, 1990.
  • [We] D. Weiß, Numerische Simulation von Temperaturfeldern bei Schweißvorgängen, Forschungsbericht, TU Magdeburg, 1991.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv29z1p85bwm
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