Applying the hp-d version of the FEM to locally enhance dimensionally reduced models

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 37-40 SPEC. ISS., 2007, Pages 3524-3533

  Duster A ^a   Niggl, A ^a   Rank, E ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

hp d method; Model adaptivity

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONTINUUM MECHANICS; DOMAIN DECOMPOSITION METHODS; MATHEMATICAL MODELS;

MODEL ADAPTIVITY; REISSNER-MINDLIN PLATE;

FINITE ELEMENT METHOD;

APPROXIMATION THEORY; COMPUTER SIMULATION; CONTINUUM MECHANICS; DOMAIN DECOMPOSITION METHODS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS;

EID: 34447103175     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.10.018     Document Type: Article

References (36)

1. Vogelius M., and Babuška I. On a dimensional reduction method. I. The optimal selection of basis function. Math. Comput. 37 (1981) 31-46
2. Vogelius M., and Babuška I. On a dimensional reduction method. II. Some approximation-theoretic results. Math. Comput. 37 (1981) 47-48
3. Vogelius M., and Babuška I. On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach. Math. Comput. 37 (1981) 361-384
4. Szabó B., and Sahrmann G. Hierarchic plate and shell models based on p-extension. Int. J. Numer. Methods Engrg. 26 (1988) 1855-1881
5. Szabó B., and Babuška I. Finite Element Analysis (1991), John Wiley & Sons
6. Szabó B., Düster A., and Rank E. The p-version of the finite element method. In: Stein E., de Borst R., and Hughes T. (Eds). Encyclopedia of Computational Mechanics vol. 1 (2004), John Wiley & Sons 119-139 (Chapter 5)
7. Düster A., Bröker H., and Rank E. The p-version of the finite element method for three-dimensional curved thin walled structures. Int. J. Numer. Methods Engrg. 52 (2001) 673-703
8. 2 flow theory with non-linear isotropic hardening. Int. J. Numer. Methods Engrg. 53 (2002) 49-63
9. Düster A., Niggl A., Nübel V., and Rank E. A numerical investigation of high-order finite elements for problems of elasto-plasticity. J. Sci. Comput. 17 (2002) 429-437
10. A. Düster, A. Niggl, E. Rank, Thermo-elastic computations of geometrically non-linear three-dimensional thin-walled continua based on high order finite elements, in: H. Mang, F. Rammerstorfer, J. Eberhardsteiner (Eds.), Proceedings of the Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002.
11. A. Düster, High order finite elements for three-dimensional, thin-walled nonlinear continua, Ph.D. thesis, Lehrstuhl für Bauinformatik, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München. 2001.
12. Düster A., Hartmann S., and Rank E. p-fem applied to finite isotropic hyperelastic bodies. Comput. Methods Appl. Mech. Engrg. 192 (2003) 5147-5166
13. Muthler A., Düster A., Volk W., Wagner M., and Rank E. High order thin-walled solid finite elements applied to elastic spring-back computations. Comput. Methods Appl. Mech. Engrg. 195 (2006) 5377-5389
14. Rank E., Düster A., Nübel V., Preusch K., and Bruhns O. High order finite elements for shells. Comput. Methods Appl. Mech. Engrg. 194 (2005) 2494-2512
15. A. Düster, D. Scholz, E. Rank, pq-Adaptive solid finite elements for three-dimensional plates and shells, Comput. Methods Appl. Mech. Engrg., submitted for publication.
16. A. Düster, D. Scholz, E. Rank, Fluid-structure interaction using high-order anisotropic solid elements, in: Proceedings of the 5th International Conference on Computation of Shell and Spatial Structures, Salzburg, Austria, 2005.
17. Scholz D., Kollmannsberger S., Düster A., and Rank E. Thin solids for fluid-structure interaction. In: Bungartz H., and Schäfer M. (Eds). Fluid-Structure Interaction, Modelling Simulation and Optimisation. Lecture Notes in Computational Science and Engineering vol. 53 (2006), Springer 294-335
18. Schwab C. A-posteriori modeling error estimation for hierarchic plate models. Numer. Math. 74 (1996) 221-259
19. Oden J., and Cho J. Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures. Comput. Methods Appl. Mech. Engrg. 136 (1996) 317-345
20. Stein E., and Ohnimus S. Coupled model- and solution-adaptivity in the finite-element method. Comput. Methods Appl. Mech. Engrg. 150 (1997) 327-350
21. Stein E., and Ohnimus S. Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems. Comput. Methods Appl. Mech. Engrg. 176 (1999) 363-385
22. Stein E., and Rüter M. Finite element methods for elasticity with error-controlled discretization and model adaptivity. In: Stein E., de Borst R., and Hughes T. (Eds). Encyclopedia of Computational Mechanics vol. 2 (2004), John Wiley & Sons 5-58 (Chapter 2)
23. Rank E. Adaptive remeshing and h-p domain decomposition. Comput. Methods Appl. Mech. Engrg. 101 (1992) 299-313
24. E. Rank, A combination of hp-version finite elements and a domain decomposition method, in: Proceedings of the First European Conference on Numerical Methods in Engineering, Brüssel, 1992.
25. Rank E. A zooming-technique using a hierarchical hp-version of the finite element method. In: Whiteman J. (Ed). The Mathematics of Finite Elements and Applications-Highlights 1993 (1993), Elsevier, Uxbridge
26. R. Krause, Multiscale Computations with a Combined h- and p-version of the Finite-element Method, Ph.D. Thesis, Fach Numerische Methoden und Informationsverarbeitung, Universität Dortmund, 1996.
27. Krause R., and Rank E. Multiscale computations with a combination of the h- and p-versions of the finite-element method. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3959-3983
28. Fish J. The s-version of the finite element method. Comput. Struct. 43 3 (1992) 539-547
29. Fish J., and Nath A. Adaptive and hierarchical modelling of fatigue crack propagation. Int. J. Numer. Methods Engrg. 36 (1993) 2825-2836
30. Fish J., and Markolefas S. Adaptive s-method for linear elastostatics. Comput. Methods Appl. Mech. Engrg. 104 (1993) 363-396
31. Fish J., and Markolefas S. Adaptive global-local refinement strategy based on the interior error estimates of the h-method. Int. J. Numer. Methods Engrg. 37 (1994) 827-838
32. Fish J., Pandheeradi M., and Belsky V. An efficient multilevel solution scheme for large scale non-linear systems. Int. J. Numer. Methods Engrg. 38 (1995) 1597-1610
33. Rank E., and Krause R. A-posteriori-Fehlerschätzung bei Multi-Skalen-Problemen. ZAMM 75 (1995) SI
34. Rank E., and Krause R. A multiscale finite-element-method. Comput. Struct. 64 (1997) 139-144
35. A. Düster, E. Rank, G. Steinl, W. Wunderlich, A combination of an h- and p-version of the finite element method for elastic-plastic problems, in: Proceedings of ECCM '99, European Conference on Computational Mechanics, München, Germany, 1999.
36. D. Scholz, An anisotropic p-adaptive method for linear elastostatic and elastodynamic analysis of thin-walled and massive structures, Dissertation, Lehrstuhl für Bauinformatik, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München, 2006.