Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
|
|
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Page(s) | 191 - 225 | |
DOI | https://doi.org/10.1051/m2an/2022067 | |
Published online | 19 January 2023 |
- D. Arnold, Finite Element Exterior Calculus. SIAM (2018). [Google Scholar]
- D.A. Di Pietro, J. Droniou and F. Rapetti, Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. Math. Models Methods Appl. Sci. 30 (2020) 1809–1855. [CrossRef] [MathSciNet] [Google Scholar]
- D.A. Di Pietro and J. Droniou, An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence. J. Comput. Phys. 429 (2021) 109991. [CrossRef] [Google Scholar]
- D.A. Di Pietro and A. Ern, Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. Math. Comp. 79 (2010) 1303–1330. [CrossRef] [MathSciNet] [Google Scholar]
- D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin methods. Vol. 69. Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012) xviii+384. [Google Scholar]
- P.F. Antonietti, A. Cangiani, J. Collis, Z. Dong, E.H. Georgoulis, S. Giani and P. Houston, Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. In: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lect. Notes Comput. Sci. Eng. Vol. 114. Springer, Cham (2016) 279–308. [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini and A. Russo, Basic principles of virtual element methods. Math. Models Methods Appl. Sci. (M3AS). 23 (2013) 199–214. [CrossRef] [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, L.D. Marini and A. Russo, The Hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci. 24 (2014) 1541–1573. [CrossRef] [MathSciNet] [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]
- B. Cockburn, D.A. Di Pietro and A. Ern, Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. ESAIM: Math. Model. Numer. Anal. 50 (2016) 635–650. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- D.A. Di Pietro and J. Droniou, The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications. Modeling, Simulation and Application. Vol. 19. Springer International Publishing (2020). [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, L.D. Marini and A. Russo, H(div) and H(curl)-conforming VEM. Numer. Math. 133 (2016) 303–332. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini and A. Russo, A family of three-dimensional virtual elements with applications to magnetostatics. SIAM J. Numer. Anal. 56 (2018) 2940–2962. [CrossRef] [MathSciNet] [Google Scholar]
- D.A. Di Pietro and J. Droniou, An arbitrary-order discrete de Rham complex on polyhedral meshes: exactness, Poincaré inequalities, and consistency. Found. Comput. Math. (2021). https://doi.org/10.1007/s10208-021-09542-8. [Google Scholar]
- D.A. Di Pietro, J. Droniou and S. Pitassi, Cohomology of the discrete de Rham complex on domains of general topology (2022). https://arxiv.org/abs/2209.00957. [Google Scholar]
- L. Beirão da Veiga, F. Dassi, D.A. Di Pietro and J. Droniou, Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes. Comput. Meth. Appl. Mech. Eng. 397 (2022) 115061. [CrossRef] [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini and A. Russo, Serendipity virtual elements for general elliptic equations in three dimensions. Chin. Ann. Math. Ser. B 39 (2018) 315–334. [CrossRef] [Google Scholar]
- D.A. Di Pietro, Cell centered Galerkin methods for diffusive problems. ESAIM: Math. Model. Numer. Anal. 46 (2012) 111–144. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- J. Droniou, R. Eymard, T. Gallouët, C. Guichard and R. Herbin, The Gradient Discretisation Method. Mathematics & Applications.. Vol. 82. Springer (2018) 511. [Google Scholar]
- R. Eymard, T. Gallouët and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces. IMA J. Numer. Anal. 30 (2010) 1009–1043. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, L.D. Marini and A. Russo, Serendipity face and edge VEM spaces. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 28 (2017) 143–180. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirão da Veiga, F. Brezzi, F. Dassi, L.D. Marini and A. Russo, Lowest order virtual element approximation of magnetostatic problems. Comput. Methods Appl. Mech. Eng. 332 (2018) 343–362. [CrossRef] [Google Scholar]
- A. Gillette, K. Hu and S. Zhang, Nonstandard finite element de Rham complexes on cubical meshes. BIT Numer. Math. 60 (2020) 373–409. [CrossRef] [Google Scholar]
- D.A. Di Pietro and J. Droniou, A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes. Comput. Math. Appl. 125 (2022) 136–149. [CrossRef] [MathSciNet] [Google Scholar]
- L. Beirão da Veiga, L. Mascotto and J. Meng, Interpolation and stability estimates for edge and face virtual elements of general order. Preprint arXiv:2203.00303 (2022). [Google Scholar]
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