Open Access
Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
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Page(s) | 3091 - 3114 | |
DOI | https://doi.org/10.1051/m2an/2021081 | |
Published online | 24 December 2021 |
- F. Bonaldi, D.A. Di Pietro, G. Geymonat and F. Krasucki, A hybrid high-order method for Kirchhoff-Love plate bending problems. ESAIM: M2AN 52 (2018) 393–421. [CrossRef] [EDP Sciences] [Google Scholar]
- S.C. Brenner and M. Neilan, A C0 interior penalty method for a fourth order elliptic singular perturbation problem. SIAM J. Numer. Anal. 49 (2011) 869–892. [Google Scholar]
- E. Burman and A. Ern, An unfitted hybrid high-order method for elliptic interface problems. SIAM J. Numer. Anal. 56 (2018) 1525–1546. [CrossRef] [MathSciNet] [Google Scholar]
- E. Burman, M. Cicuttin, G. Delay and A. Ern, An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. SIAM J. Sci. Comput. 43 (2021) A859–A882. [CrossRef] [Google Scholar]
- A. Cangiani, Z. Dong, E.H. Georgoulis and P. Houston, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. SpringerBriefs in Mathematics (2017). [CrossRef] [Google Scholar]
- A. Cangiani, Z. Dong and E.H. Georgoulis, hp-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Math. Comp. 91 (2022) 1–35. [Google Scholar]
- K.L. Cascavita, F. Chouly and A. Ern, Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions. IMA J. Numer. Anal. 40 (2020) 2189–2226. [CrossRef] [MathSciNet] [Google Scholar]
- M. Cicuttin, A. Ern and N. Pignet, Hybrid High-Order Methods. A Primer with Application to Solid Mechanics. SpringerBriefs in Mathematics (2021). [CrossRef] [Google Scholar]
- B. Cockburn, D.A. Di Pietro and A. Ern, Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. ESAIM: M2AN 50 (2016) 635–650. [CrossRef] [EDP Sciences] [Google Scholar]
- M. Cui and S. Zhang, On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation. J. Sci. Comput. 82 (2020) 1–15. [CrossRef] [MathSciNet] [Google Scholar]
- D.A. Di Pietro and J. Droniou, The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications. Vol. 19. Springer Nature (2020). [CrossRef] [Google Scholar]
- D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. Vol. 69 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012). [Google Scholar]
- D.A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes. Comput. Meth. Appl. Mech. Eng. 283 (2015) 1–21. [CrossRef] [Google Scholar]
- D.A. Di Pietro, A. Ern and S. Lemaire, An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput. Meth. Appl. Math. 14 (2014) 461–472. [CrossRef] [Google Scholar]
- Z. Dong and A. Ern, Hybrid high-order and weak Galerkin methods for the biharmonic problem. Preprint arXiv:2103.16404 (2021). [Google Scholar]
- A. Ern and J.-L. Guermond, Finite element quasi-interpolation and best approximation. ESAIM: M2AN 51 (2017) 1367–1385. [EDP Sciences] [Google Scholar]
- A. Ern and J.-L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs. Vol. 73 of Texts in Applied Mathematics. Springer Nature, Cham, Switzerland (2021). [Google Scholar]
- A. Ern and J.-L. Guermond, Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and H1+r, r > 0, regularity. Found. Comput. Math. (Published online) (2021) hal-01964299. [Google Scholar]
- J. Guzmán, D. Leykekhman and M. Neilan, A family of non-conforming elements and the analysis of Nitsche’s method for a singularly perturbed fourth order problem. Calcolo 49 (2012) 95–125. [CrossRef] [MathSciNet] [Google Scholar]
- X. Huang, Y. Shi and W. Wang, A Morley–Wang–Xu element method for a fourth order elliptic singular perturbation problem. J. Sci. Comput. 87 (2021) 1–24. [CrossRef] [Google Scholar]
- T. Nilssen, X.C. Tai and R. Winther, A robust nonconforming H2-element. Math. Comp. 70 (2001) 489–505. [Google Scholar]
- C. Talischi, G.H. Paulino, A. Pereira and I.F.M. Menezes, Polymesher: a general-purpose mesh generator for polygonal elements written in Matlab. Struct. Multidisc. Optim. 45 (2012) 309–328. [CrossRef] [Google Scholar]
- A. Veeser and R. Verfürth, Poincaré constants for finite element stars. IMA J. Numer. Anal. 32 (2012) 30–47. [CrossRef] [MathSciNet] [Google Scholar]
- M. Wang and X. Meng, A robust finite element method for a 3-D elliptic singular perturbation problem. J. Comput. Math. 25 (2007) 631–644. [MathSciNet] [Google Scholar]
- M. Wang, J. Xu and Y. Hu, Modified Morley element method for a fourth order elliptic singular perturbation problem. J. Comput. Math. 24 (2006) 113–120. [Google Scholar]
- L. Wang, Y. Wu and X. Xie, Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems. Num. Meth. Part. Diff. Equ. 29 (2013) 721–737. [CrossRef] [Google Scholar]
- W. Wang, X. Huang, K. Tang and R. Zhou, Morley–Wang–Xu element methods with penalty for a fourth order elliptic singular perturbation problem. Adv. Comp. Math. 44 (2018) 1041–1061. [CrossRef] [Google Scholar]
- H. Wu and Y. Xiao, An unfitted hp-interface penalty finite element method for elliptic interface problems. J. Comput. Math. 37 (2019) 316–339. [CrossRef] [MathSciNet] [Google Scholar]
- B. Zhang, J. Zhao and S. Chen, The nonconforming virtual element method for fourth-order singular perturbation problem. Adv. Comp. Math. 46 (2020) 1–23. [CrossRef] [Google Scholar]
- W. Zheng and H. Qi, On Friedrichs-Poincaré-type inequalities. J. Math. Anal. Appl. 304 (2005) 542–551. [CrossRef] [MathSciNet] [Google Scholar]
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