Some estimates for h-p-k-refinement in Isogeometric Analysis

Numerische Mathematik

Volumn 118, Issue 2, 2011, Pages 271-305

  Beirao da Veiga L ^a   Buffa, A ^b   Rivas, J ^c   Sangalli, G ^d  

^a Dipartimento di Matematica F Enriques   (Italy)

^b CNR   (Italy)

^c UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^d UNIVERSITY OF PAVIA   (Italy)

Author keywords

65N15

Indexed keywords

EID: 79955936082     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-010-0338-z     Document Type: Article

References (20)

1. Auricchio F., Beirão da Veiga L., Buffa A., Lovadina C., Reali A., Sangalli G.: A fully "locking-free" isogeometric approach for plane linear elasticity problems: a stream function formulation. Comput. Methods Appl. Mech. Eng. 197, 160-172 (2007).
2. Auricchio, F., Beirão da Veiga, L., Lovadina, C., Reali, A.: The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations. Comput. Methods Appl. Mech. Eng. (2010). doi: 10. 1016/j. cma. 2008. 06. 004.
3. Bazilevs Y., Beirão da Veiga L., Cottrell J. A., Hughes T. J. R., Sangalli G.: Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math. Models Methods Appl. Sci. 16, 1031-1090 (2006).
4. Bazilevs Y., Calo V. M., Cottrell J. A., Hughes T. J. R., Reali A., Scovazzi G.: Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput. Meth. Appl. Mech. Eng. 197(1-4), 173-201 (2007).
5. Benson, D. J., Bazilevs, Y., Hsu, M. C., Hughes, T. J. R.: Isogeometric Shell Analysis: The Reissner-Mindlin Shell. ICES Technical Report 09-05 (2009).
6. Ciarlet P. G., Raviart P.-A.: Interpolation theory over curved elements, with applications to finite element methods. Comput. Meth. Appl. Mech. Eng. 1, 217-249 (1972).
7. Cottrell J. A., Reali A., Bazilevs Y., Hughes T. J. R.: Isogeometric analysis of structural vibrations. Comput. Meth. Appl. Mech. Eng. 195, 5257-5296 (2006).
8. Cottrell J. A., Hughes T. J. R., Reali A.: Studies of refinement and continuity in isogeometric structural analysis. Comput. Meth. Appl. Mech. Eng. 196, 4160-4183 (2007).
9. de Boor, C.: A practical guide to splines. In: Applied Mathematical Sciences, vol. 27, revised edn. Springer, New York (2001).
10. Davis P. J.: Interpolation and Approximation. Dover, New York (1975).
11. Dubeau F., Savoie J.: Best error bounds for odd and even degree deficient splines. SIAM J. Numer. Anal. 34(3), 1167-1184 (1997).
12. Evans, J., Bazilevs, Y., Babuska, I., Hughes, T.: N-widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method. Comput. Methods Appl. Mech. Eng. (2010).
13. Farin G. E.: NURBS Curves and Surfaces: From Projective Geometry to Practical Use. A. K. Peters, Ltd., Natick (1995).
14. Gómez H., Calo V. M., Bazilevs Y., Hughes T. J. R.: Isogeometric analysis of the Cahn-Hilliard phase-field model. Comput. Methods Appl. Mech. Eng. 197, 4333-4352 (2008).
15. Hughes T. J. R., Cottrell J. A., Bazilevs Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135-4195 (2005).
16. Hughes T. J. R., Reali A., Sangalli G.: Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. Comput. Methods Appl. Mech. Eng. 197, 4104-4124 (2008).
17. Lipton, S., Evans, J. A., Bazilevs, Y., Elguedj, T., Hughes, T. J. R.: Robustness Of Isogeometric Structural Discretizations Under Severe Mesh Distortion, ICES Technical Report 09-06 (2009).
18. Schumaker, L. L.: Spline functions: basic theory, 3rd edn. Cambridge Mathematical Library. Cambridge University Press, Cambridge (2007).
19. Schwab C.: p- and hp- Finite Element Methods. Theory and Applications in Solid and Fluid Mechanics. Oxford University Press, Oxford (1998).
20. p error bounds for Hermite interpolation and the associated Wirtinger inequalities. Constr. Approx. 13(4), 461-479 (1997).