Goal-oriented error estimation in the analysis of fluid flows with structural interactions

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 41-43, 2006, Pages 5673-5684

  Grätsch, Thomas ^a   Bathe, Klaus Jürgen ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

FSI; Goal oriented error estimation; Interactions; Navier Stokes fluid flow; Nonlinear structures

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; ESTIMATION; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS;

GOAL-ORIENTED ERROR ESTIMATION; NAVIER-STOKES FLUID FLOW; NONLINEAR STRUCTURES; STRUCTURAL INTERACTIONS;

FLUID STRUCTURE INTERACTION;

COMPUTER SIMULATION; ERROR ANALYSIS; ESTIMATION; FLUID STRUCTURE INTERACTION; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS;

EID: 33745334503     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.10.020     Document Type: Article

References (28)

1. J.H. Argyris, S. Kelsey, Energy theorems and structural analysis, Aircraft Engineering, vols. 26-27 (October 1954 to May 1955), Part I is by J.H. Argyris, and Part II is by J.H. Argyris and S. Kelsey.
2. J.H. Argyris, Continua and discontinua, in: Proc. of the Conference on Matrix Methods in Structural Mechanics (Wright-Patterson A.F.B., Ohio, 1965) 11-189.
3. In: Bathe K.J. (Ed). Computational Fluid and Solid Mechanics 2003 (2003), Elsevier
4. In: Bathe K.J. (Ed). Computational Fluid and Solid Mechanics 2005 (2005), Elsevier
5. Shangguan W.B., and Lu Z.H. Experimental study and simulation of a hydraulic engine mount with fully coupled fluid structure interaction finite element analysis model. Comput. Struct. 82 (2004) 1751-1771
6. Zhang H., Zhang X., Ji S., Guo Y., Ledezma G., Elabbasi N., and deCougny H. Recent development of fluid-structure interaction capabilities in the ADINA system. Comput. Struct. 81 (2003) 1071-1085
7. Kaazempur-Mofrad M.R., Bathe M., Karcher H., Younis H.F., Seong H.C., Shim E.B., Chan R.C., Hinton D.P., Isasi A.G., Upadhyaya A., Powers M.J., Griffith L.G., and Kamm R.D. Role of simulation in understanding biological systems. Comput. Struct. 81 (2003) 715-726
8. Bathe K.J., and Pontaza J. A flow-condition-based interpolation mixed finite element procedure for higher Reynolds number fluid flow. Math. Models Methods Appl. Sci. 12 (2002) 1-15
9. Bathe K.J., and Zhang H. A flow-condition-based interpolation finite element procedure for incompressible fluid flows. Comput. Struct. 80 (2002) 1267-1277
10. Kohno H., and Bathe K.J. Insight into the flow-condition-based interpolation finite element approach: solution of steady-state advection-diffusion problems. Int. J. Numer. Methods Engrg. 63 (2005) 197-217
11. Babuška I., and Miller A.D. The post-processing approach in the finite element method, I: calculations of displacements, stresses and other higher derivatives of the displacement. Int. J. Numer. Methods Engrg. 20 (1984) 1085-1109
12. Estep D. A posteriori error bounds and global error control for approximations of ordinary differential equations. SIAM J. Numer. Anal. 32 (1995) 148
13. Eriksson K., Estep D., Hansbo P., and Johnson C. Introduction to adaptive methods for differential equations. Acta Numer. 4 (1995) 105-158
14. Becker R., and 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
15. Rannacher R., and Suttmeier F.T. A feed-back approach to error control in finite element methods: application to linear elasticity. Comput. Mech. 19 (1997) 434-446
16. Paraschivoiu M., Peraire J., and Patera A. A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations. Comput. Methods Appl. Mech. Engrg. 150 (1997) 289-312
17. Paraschivoiu M., and Patera A. A hierarchical duality approach to bounds for the outputs of partial differential equations. Comput. Methods Appl. Mech. Engrg. 158 (1998) 389-407
18. Oden J.T., and Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method. Comput. Math. Appl. 41 (2001) 735-756
19. Bangerth W., and Rannacher R. Adaptive Finite Element Methods for Differential Equations (2003), Birkhäuser, Basel
20. Grätsch T., and Bathe K.J. A posteriori error estimation techniques in practical finite element analysis. Comput. Struct. 83 (2005) 235-265
21. Grätsch T., and Bathe K.J. Influence functions and goal-oriented error estimation for finite element analysis of shell structures. Int. J. Numer. Methods Engrg. 63 (2005) 631-788
22. Oden J.T., and Prudhomme S. Estimation of modeling error in computational mechanics. J. Comput. Phys. 182 (2002) 496-515
23. Bathe K.J. ADINA system. Encycloped. Math. 11 (1997) 33-35. see also
24. Bathe K.J., and Zhang H. Finite element developments for general fluid flows with structural interactions. Int. J. Numer. Methods Engrg. 60 (2004) 213-232
25. Bathe K.J. Finite Element Procedures (1996), Prentice Hall, Upper Saddle River, NJ, USA
26. H. Kohno, K.J. Bathe, A 9-node quadrilateral FCBI element for incompressible Navier-Stokes flows, Commun. Numer. Methods Engrg., submitted for publication.
27. Kohno H., and Bathe K.J. A flow-condition-based interpolation finite element procedure for triangular grids. Int. J. Numer. Methods Fluids 49 (2005) 849-875
28. B. Banijamali, K.J. Bathe, The CIP method embedded in finite element discretizations of incompressible fluid flows, to be submitted.