Open Access
Volume 57, Number 2, March-April 2023
Page(s) 921 - 952
Published online 07 April 2023
  1. L. Beirão da Veiga, D. Cho, L. Pavarino and S. Scacchi, BDDC preconditioners for isogeometric analysis. Math. Models Methods Appl. Sci. 23 (2013) 1099–1142. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.H. Bramble, A proof of the inf-sup condition for the Stokes equations on Lipschitz domains. Math. Models Methods Appl. Sci. 13 (2003) 361–371. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Bressan and B. Jüttler, Inf–sup stability of isogeometric Taylor-Hood and Sub-Grid methods for the Stokes problem with hierarchical splines. IMA J. Numer. Anal. 38 (2018) 955–975. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bressan and G. Sangalli, Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique. IMA J. Numer. Anal. 33 (2013) 629–651. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising form Lagrange multipliers. RAIRO 8 (1974) 129–151. [Google Scholar]
  6. A. Buffa, C. De Falco and G. Sangalli, Isogeometric analysis: stable elements for the 2D Stokes equation. Int. J. Numer. Methods Fluids 65 (2011) 1407–1422. [Google Scholar]
  7. M. Costabel, M. Crouzeix, M. Dauge and Y. Lafranche, The inf-sup constant for the divergence on corner domains. Numer. Methods Part. Differ. Equ. 31 (2015) 439–458. [CrossRef] [Google Scholar]
  8. J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis – Toward Integration of CAD and FEA. John Wiley & Sons (2009). [CrossRef] [Google Scholar]
  9. J.A. Evans and T.J.R. Hughes, Isogeometric divergence-conforming B-splines for the Darcy–Stokes–Brinkman equations. Math. Models Methods Appl. Sci. 23 (2013) 671–741. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson and D. Rixen, FETI-DP: a dual–primal unified FETI method-part I: a faster alternative to the two-level FETI method. Int. J. Numer. Methods Eng. 50 (2001) 1523–1544. [CrossRef] [Google Scholar]
  11. M. Fortin and F. Brezzi, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). [Google Scholar]
  12. C. Hofer and U. Langer, Dual-primal isogeometric tearing and interconnecting solvers for multipatch dG-IgA equations. Comput. Methods Appl. Mech. Eng. 316 (2017) 2–21. [CrossRef] [Google Scholar]
  13. C. Hofer and U. Langer, Dual-primal isogeometric tearing and interconnecting methods, in Contributions to Partial Differential Equations and Applications. Springer (2019) 273–296. [CrossRef] [Google Scholar]
  14. T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194 (2005) 4135–4195. [CrossRef] [Google Scholar]
  15. H.H. Kim, C.-O. Lee and E.-H. Park, A FETI-DP formulation for the Stokes problem without primal pressure components. SIAM J. Numer. Anal. 47 (2010) 4142–4162. [CrossRef] [MathSciNet] [Google Scholar]
  16. S.K. Kleiss, C. Pechstein, B. Jüttler and S. Tomar, IETI-isogeometric tearing and interconnecting. Comput. Methods Appl. Mech. Eng. 247 (2012) 201–215. [CrossRef] [Google Scholar]
  17. J. Li, A dual-primal FETI method for incompressible Stokes equations. Numer. Math. 102 (2005) 257–275. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Mandel, C.R. Dohrmann and R. Tezaur, An algebraic theory for primal and dual substructuring methods by constraints. Appl. Numer. Math. 54 (2005) 167–193. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Necas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). [Google Scholar]
  20. L.F. Pavarino and S. Scacchi, Isogeometric block FETI-DP preconditioners for the Stokes and mixed linear elasticity systems. Comput. Methods Appl. Mech. Eng. 310 (2016) 694–710. [CrossRef] [Google Scholar]
  21. C. Pechstein, Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems. Springer, Heidelberg (2013). [CrossRef] [Google Scholar]
  22. R. Schneckenleitner and S. Takacs, Condition number bounds for IETI-DP methods that are explicit in h and p. Math. Models Methods Appl. Sci. 30 (2020) 2067–2103. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Schneckenleitner and S. Takacs, IETI-DP methods for discontinuous Galerkin multi-patch Isogeometric Analysis with T-junctions. Comput. Methods Appl. Mech. Eng. 393 (2022) 114694. [CrossRef] [Google Scholar]
  24. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  25. J. Sogn and S. Takacs, Dual-primal isogeometric tearing and interconnecting methods for the Stokes problem, in Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1, edited by J.M. Melenk, I. Perugia, J. Schöberl and C. Schwab. Springer (to appear) (2023). [Google Scholar]
  26. X. Tu and J. Li, A unified dual-primal finite element tearing and interconnecting approach for incompressible Stokes equations. Int. J. Numer. Methods Eng. 94 (2013) 128–149. [CrossRef] [Google Scholar]
  27. X. Tu and J. Li, A FETI-DP type domain decomposition algorithm for three-dimensional incompressible Stokes equations. SIAM J. Numer. Anal. 53 (2015) 720–742. [CrossRef] [MathSciNet] [Google Scholar]
  28. O. Widlund, S. Zampini, S. Scacchi and L.F. Pavarino, Block FETI–DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity. Math. Comput. 90 (2021) 1773–1797. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you