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Volumn 51, Issue 4 SPEC. ISS., 2004, Pages 511-533

Anisotropic mesh adaptation in computational fluid dynamics: Application to the advection-diffusion-reaction and the Stokes problems

Author keywords

A posteriori error estimators; Advection diffusion reaction problem; Anisotropic mesh adaption; Computational fluid dynamics; Finite element methods; Stokes problem

Indexed keywords

ADAPTIVE ALGORITHMS; DIFFUSION; ERROR ANALYSIS; FINITE ELEMENT METHOD; INTERPOLATION; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; REACTION KINETICS;

EID: 7544240625     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.06.007     Document Type: Conference Paper
Times cited : (90)

References (35)
  • 2
    • 0003267718 scopus 로고    scopus 로고
    • Anisotropic finite elements: Local estimates and applications
    • Stuttgart: Teubner
    • Apel T. Anisotropic Finite Elements: Local Estimates and Applications. Advances in Numerical Mathematics. 1999;Teubner, Stuttgart.
    • (1999) Advances in Numerical Mathematics
    • Apel, T.1
  • 3
    • 0030503035 scopus 로고    scopus 로고
    • Anisotropic mesh refinement in stabilized Galerkin methods
    • Apel T., Lube G. Anisotropic mesh refinement in stabilized Galerkin methods. Numer. Math. 74:1996;261-282.
    • (1996) Numer. Math. , vol.74 , pp. 261-282
    • Apel, T.1    Lube, G.2
  • 5
    • 0003170104 scopus 로고
    • Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes
    • Becker R., Rannacher R. Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes. Notes Numer. Fluid Mech. 49:1995;52-62.
    • (1995) Notes Numer. Fluid Mech. , vol.49 , pp. 52-62
    • Becker, R.1    Rannacher, R.2
  • 6
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: Basic analysis and examples
    • Becker R., Rannacher R. A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math. 4:1996;237-264.
    • (1996) East-West J. Numer. Math. , vol.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 7
    • 0001078341 scopus 로고
    • Choosing bubbles for advection-diffusion problems
    • Brezzi F., Russo A. Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4:1994;571-587.
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 571-587
    • Brezzi, F.1    Russo, A.2
  • 8
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32:1982;199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 11
    • 0037050818 scopus 로고    scopus 로고
    • Grid adaptation for functional outputs: Application to two-dimensional inviscid flows
    • Darmofal D.L., Venditti D.A. Grid adaptation for functional outputs: Application to two-dimensional inviscid flows. J. Comput. Phys. 176:(1):2002;40-69.
    • (2002) J. Comput. Phys. , vol.176 , Issue.1 , pp. 40-69
    • Darmofal, D.L.1    Venditti, D.A.2
  • 12
    • 84966220003 scopus 로고
    • An absolutely stabilized finite element method for the Stokes problem
    • Douglas J., Wang J. An absolutely stabilized finite element method for the Stokes problem. Math. Comp. 52:1989;495-508.
    • (1989) Math. Comp. , vol.52 , pp. 495-508
    • Douglas, J.1    Wang, J.2
  • 13
    • 84968481723 scopus 로고
    • Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems
    • Eriksson K., Johnson C. Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. Math. Comp. 60:1993;167-188.
    • (1993) Math. Comp. , vol.60 , pp. 167-188
    • Eriksson, K.1    Johnson, C.2
  • 14
    • 0035602908 scopus 로고    scopus 로고
    • New anisotropic a priori error estimates
    • Formaggia L., Perotto S. New anisotropic a priori error estimates. Numer. Math. 89:2001;641-667.
    • (2001) Numer. Math. , vol.89 , pp. 641-667
    • Formaggia, L.1    Perotto, S.2
  • 15
    • 0142118651 scopus 로고    scopus 로고
    • Anisotropic error estimates for elliptic problems
    • Formaggia L., Perotto S. Anisotropic error estimates for elliptic problems. Numer. Math. 94:2003;67-92.
    • (2003) Numer. Math. , vol.94 , pp. 67-92
    • Formaggia, L.1    Perotto, S.2
  • 17
    • 78649468088 scopus 로고    scopus 로고
    • Anisotropic mesh adaption with application to CFD problems
    • H.A. Mang, F.G. Rammerstofer, & J. Eberhardsteiner. Fifth World Congress on Computational Mechanics, Vienna, Austria
    • Formaggia L., Micheletti S., Perotto S. Anisotropic mesh adaption with application to CFD problems. Mang H.A., Rammerstofer F.G., Eberhardsteiner J. Proceedings of WCCMV, Fifth World Congress on Computational Mechanics, Vienna, Austria. 2002.
    • (2002) Proceedings of WCCMV
    • Formaggia, L.1    Micheletti, S.2    Perotto, S.3
  • 18
    • 0037849049 scopus 로고    scopus 로고
    • An anisotropic a posteriori error estimate for a convection-diffusion problem
    • Formaggia L., Perotto S., Zunino P. An anisotropic a posteriori error estimate for a convection-diffusion problem. Comput. Visual. Sci. 4:2001;99-104.
    • (2001) Comput. Visual. Sci. , vol.4 , pp. 99-104
    • Formaggia, L.1    Perotto, S.2    Zunino, P.3
  • 19
    • 0026835579 scopus 로고
    • Stabilized finite element methods. I. Application to the advective-diffusive model
    • Franca L.P., Frey S.L., Hughes T.J.R. Stabilized finite element methods. I. Application to the advective-diffusive model. Comput. Methods Appl. Mech. Engrg. 95:1992;253-276.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.95 , pp. 253-276
    • Franca, L.P.1    Frey, S.L.2    Hughes, T.J.R.3
  • 20
    • 0027611385 scopus 로고
    • Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations
    • Franca L.P., Hughes T.J.R. Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 105:1993;285-298.
    • (1993) Comput. Methods Appl. Mech. Engrg. , vol.105 , pp. 285-298
    • Franca, L.P.1    Hughes, T.J.R.2
  • 21
    • 0026386228 scopus 로고
    • Error analysis of some GLS methods for elasticity equations
    • Franca L., Stenberg R. Error analysis of some GLS methods for elasticity equations. SIAM J. Numer. Anal. 28:1991;1680-1697.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1680-1697
    • Franca, L.1    Stenberg, R.2
  • 23
    • 84983200859 scopus 로고    scopus 로고
    • Adjoint equation in CFD: Duality, boundary conditions and solution behaviour
    • M.B. Giles, N.A. Pierce, Adjoint equation in CFD: Duality, boundary conditions and solution behaviour, AIAA Paper 97-1850, 1997.
    • (1997) AIAA Paper , vol.97 , Issue.1850
    • Giles, M.B.1    Pierce, N.A.2
  • 24
    • 0013270608 scopus 로고    scopus 로고
    • Anisotropic mesh adaptation: A step towards a mesh-independent and user-independent CFD
    • V. Venkatakrishnan, M.D. Salas, & S.R. Chakravarthy. Dordrecht: Kluwer Academic
    • Habashi W.G., Fortin M., Dompierre J., Vallet M.G., Bourgault Y. Anisotropic mesh adaptation: A step towards a mesh-independent and user-independent CFD. Venkatakrishnan V., Salas M.D., Chakravarthy S.R. Barriers and Challenges in Computational Fluid Dynamics. 1998;99-117 Kluwer Academic, Dordrecht.
    • (1998) Barriers and Challenges in Computational Fluid Dynamics , pp. 99-117
    • Habashi, W.G.1    Fortin, M.2    Dompierre, J.3    Vallet, M.G.4    Bourgault, Y.5
  • 26
    • 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 T.J.R., Franca L., Balestra M. 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. Engrg. 59:1986;85-99.
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.59 , pp. 85-99
    • Hughes, T.J.R.1    Franca, L.2    Balestra, M.3
  • 28
    • 0035567411 scopus 로고    scopus 로고
    • Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes
    • Kunert G. Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes. Adv. Comput. Math. 15:2001;237-259.
    • (2001) Adv. Comput. Math. , vol.15 , pp. 237-259
    • Kunert, G.1
  • 29
    • 7544238098 scopus 로고    scopus 로고
    • Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator
    • MOX, Modelling and Scientific Computing, Dept. of Math. F. Brioschi, Politecnico di Milano, submitted for publication
    • S. Micheletti, S. Perotto, Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator, MOX, Modelling and Scientific Computing, Dept. of Math. F. Brioschi, Politecnico di Milano, 2004. Comput. Methods Appl. Mech. Engrg., submitted for publication.
    • (2004) Comput. Methods Appl. Mech. Engrg.
    • Micheletti, S.1    Perotto, S.2
  • 30
    • 3142737182 scopus 로고    scopus 로고
    • Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and Stokes problems
    • Micheletti S., Perotto S., Picasso M. Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and Stokes problems. SIAM J. Numer. Anal. 41:(3):2003;1131-1162.
    • (2003) SIAM J. Numer. Anal. , vol.41 , Issue.3 , pp. 1131-1162
    • Micheletti, S.1    Perotto, S.2    Picasso, M.3
  • 31
    • 3142675792 scopus 로고    scopus 로고
    • Some remarks on the stability coefficients and bubble stabilization of FEM on anisotropic grids
    • MOX - Modeling and Scientific Computing, Department of Mathematics "F. Brioschi", Politecnico di Milano
    • S. Micheletti, S. Perotto, M. Picasso, Some remarks on the stability coefficients and bubble stabilization of FEM on anisotropic grids, MOX Report 06, MOX - Modeling and Scientific Computing, Department of Mathematics "F. Brioschi", Politecnico di Milano, 2002.
    • (2002) MOX Report , vol.6
    • Micheletti, S.1    Perotto, S.2    Picasso, M.3
  • 32
    • 0034234180 scopus 로고    scopus 로고
    • On the performance of high aspect ratio elements for incompressible flows
    • Mittal S. On the performance of high aspect ratio elements for incompressible flows. Comput. Methods Appl. Mech. Engrg. 188:2000;269-287.
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.188 , pp. 269-287
    • Mittal, S.1
  • 34
    • 0039774368 scopus 로고    scopus 로고
    • A posteriori error estimation in least-squares stabilized finite element schemes
    • Rannacher R. A posteriori error estimation in least-squares stabilized finite element schemes. Comput. Methods Appl. Mech. Engrg. 166:1998;99-114.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.166 , pp. 99-114
    • Rannacher, R.1
  • 35
    • 0030530686 scopus 로고    scopus 로고
    • An a posteriori error estimator for anisotropic refinement
    • Siebert K.G. An a posteriori error estimator for anisotropic refinement. Numer. Math. 73:1996;373-398.
    • (1996) Numer. Math. , vol.73 , pp. 373-398
    • Siebert, K.G.1


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