Open Access
Volume 56, Number 6, November-December 2022
Page(s) 2081 - 2103
Published online 03 November 2022
  1. P.F. Antonietti, G. Manzini and M. Verani, The conforming virtual element method for polyharmonic problems. Comput. Math. Appl. 79 (2020) 2021–2034. [CrossRef] [MathSciNet] [Google Scholar]
  2. S. Balay et al., PETSc Web page. (2021). [Google Scholar]
  3. J.W. Barrett, S. Langdon and R. Nürnberg, Finite element approximation of a sixth order nonlinear degenerate parabolic equation. Numer. Math. 96 (2004) 401–434. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.H. Bramble and M. Zlámal, Triangular elements in the finite element method. Math. Comput. 24 (1970) 809–820. [CrossRef] [Google Scholar]
  5. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy. J. Chem. Phys. 28 (1958) 258–267. [Google Scholar]
  6. A.S. Chang and W. Chen, A note on a class of higher order comformally covariant equations. Discrete Continuous Dyn. Syst. 7 (2001) 275–281. [CrossRef] [Google Scholar]
  7. L. Chen and X. Huang, Nonconforming virtual element method for 2mth order partial differential equations in ℝn. Math. Comput. 89 (2020) 1711–1744. [Google Scholar]
  8. H. Chen, A. Pani and W. Qiu, A mixed finite element scheme for biharmonic equation with variable coefficient and von Kármán equations. Preprint: arXiv:2005.11734 (2020). [Google Scholar]
  9. M. Cheng and J.A. Warren, An efficient algorithm for solving the phase field crystal model. J. Comput. Phys. 227 (2008) 6241–6248. [CrossRef] [MathSciNet] [Google Scholar]
  10. C.M. Elliott and S. Zheng, On the Cahn-Hilliard equation. Arch. Ration. Mech. Anal. 96 (1986) 339–357. [Google Scholar]
  11. G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei and R.L. Taylor, Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput. Methods Appl. Mech. Eng. 191 (2002) 3669–3750. [Google Scholar]
  12. T. Gudi, A new error analysis for discontinuous finite element methods for linear elliptic problems. Math. Comput. 79 (2010) 2169–2189. [Google Scholar]
  13. T. Gudi and M. Neilan, An interior penalty method for a sixth-order elliptic equation. IMA J. Numer. Anal. 31 (2011) 1734–1753. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Hu and S. Zhang, The minimal conforming Hk finite element space on ℝn rectangular grids. Math. Comput. 84 (2015) 563–579. [Google Scholar]
  15. J. Hu and S. Zhang, A canonical construction of Hm-nonconforming triangular elements. Ann. Appl. Math. 33 (2017) 266–288. [MathSciNet] [Google Scholar]
  16. J. Hu, T. Lin and Q. Wu, A construction of Cr conforming finite element spaces in any dimension. Preprint: arXiv:2103.14924 (2021). [Google Scholar]
  17. X. Huang, Nonconforming virtual element method for 2mth order partial differential equations in ℝn with m > n. Calcolo 57 (2020) 1–38. [CrossRef] [Google Scholar]
  18. N.A. Kudryashov, Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation. Optik 206 (2020) 164335. [CrossRef] [Google Scholar]
  19. M. Schedensack, A new discretization for mth-Laplace equations with arbitrary polynomial degrees. SIAM J. Numer. Anal. 54 (2016) 2138–2162. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Süli and I. Mozolevski, hp-version interior penalty DGFEMs for the biharmonic equation. Comput. Methods Appl. Mech. Eng. 196 (2007) 1851–1863. [Google Scholar]
  21. C. Wang and S.M. Wise, An energy stable and convergent finite-difference scheme for the modified phase field crystal equation. SIAM J. Numer. Anal. 49 (2011) 945–969. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Wang and J. Xu, Minimal finite element spaces for 2m-th-order partial differential equation in ℝn. Math. Comput. 82 (2013) 25–43. [Google Scholar]
  23. S.M. Wise, C. Wang and J.S. Lowengrub, An energy-stable and convergent finite difference scheme for the phase field crystal equation. SIAM J. Numer. Anal. 47 (2009) 2269–2288. [CrossRef] [MathSciNet] [Google Scholar]
  24. S. Wu and J. Xu, Pm interior penalty nonconforming finite element methods for 2m-th order PDEs in ℝn. Preprint: arXiv:1710.07678 (2017). [Google Scholar]
  25. S. Wu and J. Xu, Nonconforming finite element spaces for 2mth order partial differential equations on ℝn simplicial grids when m = n + 1. Math. Comput. 88 (2019) 531–551. [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