Proper intrinsic scales for a-posteriori multiscale error estimation

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 33-36, 2006, Pages 3983-4001

  Hauke, Guillermo ^a   Doweidar, Mohamed H ^a   Miana, Mario ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b Division of Industrial Systems   (Spain)

Author keywords

A posteriori error estimation; Advection diffusion reaction equation; Fluid mechanics; Stabilized methods; Variational multiscale method

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; GREEN'S FUNCTION; TRANSPORT PROPERTIES;

A-POSTERIORI ERROR ESTIMATION; ADVECTION-DIFFUSION-REACTION EQUATION; FLUID TRANSPORT; STABILIZED METHODS; VARIATIONAL MULTISCALE METHOD;

FLUID MECHANICS;

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; FLUID MECHANICS; GREEN'S FUNCTION; TRANSPORT PROPERTIES;

EID: 33646179893     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.07.012     Document Type: Article

References (32)

1. Ainsworth M., and Oden J.T. A Posterior Error Estimation in Finite Element Analysis (2000), John Wiley & Sons
2. Babuška I.M., and Miller A. A feedback finite element method with a posteriori error estimation: Part 1. Comput. Methods Appl. Mech. Engrg. 61 (1987) 1-40
3. Babuška I.M., and Rheinboldt W.C. A posteriori error estimates for the finite element. Int. J. Numer. Methods Engrg. 12 (1978) 1597-1615
4. Babuška I.M., and Rheinboldt W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 18 (1978) 736-754
5. 1. Math. Comput. 33 (1979) 435-463
6. Bank R.E., and Weiser A. Some a posteriori error estimators for elliptic partial differential equations. Math. Comput. 44 (1985) 283-301
7. Brenner S.C., and Scott L.R. The Mathematical Theory of Finite Element Methods. second ed. (2002), Springer-Verlag
8. Brezzi F., Bristeau M.O., Franca L.P., Mallet M., and Rogé G. A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Comput. Methods Appl. Mech. Engrg. 96 (1992) 117-129
9. Brezzi F., Hauke G., Marini L.D., and Sangalli G. Link-cutting bubbles for the stabilization of convection-diffusion-reaction problems. Math. Models Methods Appl. Sci. 13 (2003) 445-461
10. Brezzi F., and Russo A. Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4 (1994) 571-587
11. Brezzi F., Franca L.P., Hughes T.J.R., and Russo A. b = ∫g. Comput. Methods Appl. Mech. Engrg. 145 (1997) 329-339
12. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259
13. Demkowicz L., Oden J.T., and Strouboulis T. Adaptive finite elements for flow problems with moving boundaries. Part 1: Variational principles and a posteriori error estimates. Comput. Methods Appl. Mech. Engrg. 46 (1984) 217-251
14. Franca L.P., and Russo A. Deriving upwinding, mass lumping and selective reduced integration by residual-free bubbles. Appl. Math. Lett. 9 (1996) 83-88
15. Franca L.P., and Valentin F. On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1785-1800
16. Franca L.P., Frey S.L., and Hughes T.J.R. Stabilized finite element methods: I. Application to the advective-diffusive model. Comput. Methods Appl. Mech. Engrg. 95 (1992) 253-276
17. G. Hauke, M.H. Doweidar, M. Miana, The multiscale approach to error estimation and adaptivity, Comput. Methods Appl. Mech. Engrg., in press, doi:10.1016/j.cma.2005.05.029.
18. Hauke G. A simple stabilized method for the advection-diffusion-reaction equation. Comput. Methods Appl. Mech. Engrg. 191 (2002) 2925-2947
19. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications
20. 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 (1995) 387-401
21. Hughes T.J.R., Feijoo G.R., Mazzei L., and Quincy J.B. The variational multiscale method: A paradigm for computational mechanics. Comput. Methods Appl. Mech. Engrg. 166 (1998) 3-24
22. John V. A numerical study of a posteriori error estimators for convection-diffusion equations. Comput. Methods Appl. Mech. Engrg. 190 (2000) 757-781
23. Johnson C. Adaptive finite element methods for diffusion and convection problems. Comput. Methods Appl. Mech. Engrg. 82 (1990) 301-322
24. Kelly D.W., Gago J.R., Zienkiewicz O.C., and Babuška I. A posterior error analysis and adaptive processes in the finite element method. Part I: Error analysis. Int. J. Numer. Methods Engrg. 19 (1983) 1593-1610
25. Papastavrou A., and Verfürth R. A posteriori error estimators for stationary convection-diffusion problems: a computational comparison. Comput. Methods Appl. Mech. Engrg. 189 (2000) 449-462
26. Russo A. A posteriori error estimators via bubble functions. Math. Models Methods Appl. Sci. 1 (1996) 33-41
27. Sangalli G. A robust a posteriori estimator for the Residual-free Bubbles method applied to advection-diffusion problems. Numer. Math. 89 (2001) 379-399
28. G. Sangalli, On robust a posteriori estimators for the advection-diffusion-reaction problem, ICES Report 04-55, ICES, University of Texas at Austin, 2004.
29. Verfürth R. A posteriori error estimators for the Stokes problem. Numer. Math. 55 (1989) 309-325
30. Verfürth R. A posteriori error estimators for convection-diffusion equations. Numer. Math. 80 (1998) 641-663
31. R. Verfürth, Robust a posteriori error estimates for stationary convection-diffusion equations, Technical Report Ruhr-Universität, Bochum, 2004.
32. Zienkiewicz O.C., and Zhu J.Z. A simple error estimator in the finite element method. Int. J. Numer. Methods Engrg. 24 (1987) 337-357