Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2233 - 2258
DOI https://doi.org/10.1051/m2an/2021050
Published online 13 October 2021
  1. R.A. Adams, Sobolev spaces, In Vol. 65 of Pure and Applied Mathematics, Academic Press, New York-London (1975). [Google Scholar]
  2. B. Ahmad, A. Alsaedi, F. Brezzi, L.D. Marini and A. Russo, Equivalent projectors for virtual element methods. Comput. Math. Appl. 66 (2013) 376–391. [Google Scholar]
  3. P.F. Antonietti, S. Giani and P. Houston, Hp-Version composite discontinuous Galerkin methods for elliptic problems on complicated domains. SIAM J. Sci. Comput. 35 (2013) A1417–A1439. [Google Scholar]
  4. 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. Lect. Notes Comput. Sci. Eng. 50 (2016) 699–725. [Google Scholar]
  5. B. Ayuso De Dios, K. Lipnikov and G. Manzini, The nonconforming virtual element method. ESAIM Math. Model. Numer. Anal. 50 (2016) 879–904. [Google Scholar]
  6. L. Beirão da Veiga and G. Vacca, Sharper error estimates for Virtual Elements and a bubble-enriched version (2020). [Google Scholar]
  7. 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. 23 (2013) 199–214. [Google Scholar]
  8. 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. [Google Scholar]
  9. L. Beirão da Veiga, F. Brezzi, L.D. Marini and A. Russo, Mixed virtual element methods for general second order elliptic problems on polygonal meshes. ESAIM Math. Model. Numer. Anal. 50 (2016) 727–747. [Google Scholar]
  10. L. Beirão da Veiga, F. Brezzi, L.D. Marini and A. Russo, Virtual Element Method for general second-order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26 (2016) 729–750. [Google Scholar]
  11. L. Beirão da Veiga, F. Dassi and A. Russo, High-order virtual element method on polyhedral meshes. Comput. Math. Appl. 74 (2017) 1110–1122. [Google Scholar]
  12. L. Beirão da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method. Math. Models Methods Appl. Sci. 27 (2017) 2557–2594. [Google Scholar]
  13. L. Beirão da Veiga, A. Pichler and G. Vacca, A virtual element method for the miscible displacement of incompressible fluids in porous media. Comput. Methods Appl. Mech. Eng. 375 (2021) 113649. [Google Scholar]
  14. M.F. Benedetto, S. Berrone, A. Borio, S. Pieraccini and S. Scialò, A hybrid mortar virtual element method for discrete fracture network simulations. J. Comput. Phys. 306 (2016) 148–166. [Google Scholar]
  15. M.F. Benedetto, S. Berrone, A. Borio, S. Pieraccini and S. Scialò, Order preserving SUPG stabilization for the virtual element formulation of advection-diffusion problems. Comput. Methods Appl. Mech. Eng. 293 (2016) 18–40. [Google Scholar]
  16. M.F. Benedetto, S. Berrone and S. Scialò, A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method. Finite Elem. Anal. Des. 109 (2016) 23–36. [Google Scholar]
  17. S. Berrone, A. Borio and G. Manzini, SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations. Comput. Methods Appl. Mech. Eng. 340 (2018) 500–529. [Google Scholar]
  18. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, 3rd edition. In Vol. 15 of Texts in Applied Mathematics Springer, New York (2008). [Google Scholar]
  19. S.C. Brenner and L.Y. Sung, Virtual element methods on meshes with small edges or faces. Math. Models Methods Appl. Sci. 28 (2018) 1291–1336. [Google Scholar]
  20. F. Brezzi, R. Falk and L.D. Marini, Basic principles of mixed virtual element methods. ESAIM Math. Model. Numer. Anal. 48 (2014) 1227–1240. [Google Scholar]
  21. A. Cangiani, E.H. Georgoulis and P. Houston, Hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. 24 (2014) 2009–2041. [Google Scholar]
  22. A. Cangiani, Z. Dong, E.H. Georgoulis and P. Houston, Hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM Math. Model. Numer. Anal. 50 (2016) 699–725. [Google Scholar]
  23. A. Cangiani, E.H. Georgoulis, T. Pryer and O.J. Sutton, A posteriori error estimates for the virtual element method. Numer. Math. 137 (2017) 857–893. [Google Scholar]
  24. A. Cangiani, G. Manzini and O. Sutton, Conforming and nonconforming virtual element methods for elliptic problems. IMA J. Numer. Anal. 37 (2017) 1317–1354. [Google Scholar]
  25. L. Chen and J. Huang, Some error analysis on virtual element methods. Calcolo 55 (2018). [Google Scholar]
  26. J. Coulet, I. Faille, V. Girault, N. Guy and N. Nataf, A fully coupled scheme using virtual element method and finite volume for poroelasticity. Comput. Geosci. 24 (2020) 381–403. [Google Scholar]
  27. D.A. Di Pietro and A. Ern, Hybrid high-order methods for variable-diffusion problems on general meshes. C. R. Math. Acad. Sci. Paris 353 (2015) 31–34. [Google Scholar]
  28. D.A. Di Pietro, J. Droniou and A. Ern, A discontinuous-skeletal method for advection-diffusion-reaction on general meshes. SIAM J. Numer. Anal. 53 (2015) 2135–2157. [Google Scholar]
  29. L.P. Franca, S.L. Frey and T.J.R. Hughes, Stabilized finite element methods. I. Application to the advective-diffusive model. Comput. Methods Appl. Mech. Eng. 95 (1992) 253–276. [Google Scholar]
  30. A. Fumagalli and E. Keilegavlen, Dual virtual element method for discrete fractures networks. SIAM J. Sci. Comput. 40 (2018) B228–B258. [Google Scholar]
  31. A. Fumagalli and E. Keilegavlen, Dual virtual element methods for discrete fracture matrix models. Oil Gas Sci. Technol. 74 (2019) 41. [Google Scholar]
  32. T.J.R. Hughes and A.N. Brooks, A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline-upwind procedure. Finite Elem. Fluids (1982) 47–65. [Google Scholar]
  33. A. Quarteroni and A. Valli, Numerical approximation of partial differential equations. Springer Science & Business Media, Vol. 23 (2008). [Google Scholar]

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