Adaptive computations of a posteriori finite element output bounds: A comparison of the "hybrid-flux" approach and the "flux-free" approach

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 36-38, 2004, Pages 4001-4033

  Choi, Hae Won ^a   Paraschivoiu, Marius ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Adaptive computations; Finite element output; Flux free; Hybrid flux

Indexed keywords

ADAPTIVE COMPUTATIONS; BOUND-GAP; FLUX-FREE APPROACH; NUMERICAL ACCURACY;

BOUNDARY CONDITIONS; COSTS; DECOMPOSITION; DIFFUSION; FINITE ELEMENT METHOD; HEAT CONVECTION; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVE CONTROL SYSTEMS;

FINITE ELEMENT ANALYSIS;

EID: 4344688564     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.02.012     Document Type: Article

References (23)

1. Ainsworth M. Oden J.T. A posteriori error estimation in finite element analysis Comput. Methods Appl. Mech. Engrg. 142 1997 1-80
2. Ainsworth M. Oden J.T. A Posteriori Error Estimation in Finite Element Analysis 2000 Wiley-Interscience
3. Babuška I. Melenk J.M. The partition of unity method Int. J. Numer. Meth. Engrg. 40 1997 727-758
4. Babuška I. Rheinboldt W.C. Error estimates for adaptive finite element computations SIAM J. Numer. Anal. 15 4 1978 736-754
5. Carstensen C. Funken S.A. Fully reliable localized error control in the FEM SIAM J. Sci. Comput. 21 4 2000 1465-1484
6. Cheng Z. Paraschivoiu M. Parallel computations of finite element output bounds for conjugate heat transfer Finite Elem. Anal. Des. 39 2003 581-597
7. H.-W. Choi, A posteriori finite element bounds with adaptive mesh refinement: application to outputs of the three dimensional Convection-Diffusion equation. Master's thesis, Department of Mechanical and Industrial Engineering, University of Toronto, October 2001
8. Choi H.-W. Paraschivoiu M. A posteriori finite element output bounds with adaptive mesh refinement: application to a heat transfer problem in a three-dimensional rectangular duct Comput. Methods Appl. Mech. Engrg. 191 2002 4905-4925
9. Farhat C. Roux F.-X. A method of finite tearing and interconnecting and its parallel solution algorithm Int. J. Numer. Methods Engrg. 32 1991 1205-1227
10. Farhat C. Roux F.-X. An unconventional domain decomposition method for efficient parallel solution of large-scale finite element systems SIAM J. Sci. Comput. 13 1 1992 379-396
11. Machiels L. Maday Y. Patera A.T. A "flux-free" nodal neumann subproblem approach to output bounds for partial differential equations C. R. Acad. Sci. Ser. I--Math. (Numer. Anal.) 330 2000 249-254
12. Machiels L. Maday Y. Patera A.T. Output bounds for reduced-order approximations of elliptic partial differential equations Comput. Methods Appl. Mech. Engrg. 190 2001 3413-3426
13. Machiels L. Patera A.T. Peraire J. A Posteriori finite element output bounds for the incompressible Navier-Stokes equations; application to a natural convection problem J. Comput. Phys. 172 2001 401-425
14. Maday Y. Patera A.T. Peraire J. A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem C. R. Acad. Sci. Series I--Math. (Numer. Anal.) 328 1999 823-828
15. Maday Y. Patera A.T. Numerical analysis of a posteriori finite element bounds for linear-functional outputs Math. Models Methods Appl. Sci. 10 5 2000 785-799
16. Morin P. Nochetto R.H. Siebert K.G. Local problems on stars: a posteriori error estimators, convergence, and performance Math. Comput. 72 243 2002 1067-1097
17. M. Paraschivoiu, A posteriori finite element bounds for linear-functional outputs of Coericive Partial Differential Equations and of the Stokes Problems, Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, 1997
18. Paraschivoiu M. A posteriori finite element output bounds in three space dimensions using the FETI method Comput. Methods Appl. Mech. Engrg. 190 2001 6629-6640
19. Paraschivoiu M. Patera A.T. A posteriori finite element bounds for linear-functional outputs of the stokes problem Int. J. Numer. Methods Fluids 32 2000 823-849
20. Paraschivoiu M. Patera A.T. Peraire J. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations Comput. Methods Appl. Mech. Engrg. 150 1997 289-312
21. Patera A.T. Peraire J. A General Lagrangian Formulation for the Computation of A Posteriori Finite Element Bounds, Chapter in "Error Estimation and Solution Adaptive Procedures in CFD" 2002 Springer-Verlag
22. Strang G. Introduction to Applied Mathematics 1986 Wellesley-Cambridge Press
23. Verfürth R. A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques 1996 Wiley-Teubner