Free Access
Issue
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S785 - S810
DOI https://doi.org/10.1051/m2an/2020059
Published online 26 February 2021
  1. 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: Vol.114 of Lecture notes in computational science and engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, Springer, Cham (2016) 279–308. [Google Scholar]
  2. R. Araya, C. Harder, D. Paredes and F. Valentin, Multiscale hybrid-mixed method. SIAM J. Numer. Anal. 51 (2013) 3505–3531. [Google Scholar]
  3. M. Arioli and D. Loghin, Discrete interpolation norms with applications. SIAM J. Numer. Anal. 47 (2009) 2924–2951. [Google Scholar]
  4. B. Ayuso de Dios, K. Lipnikov and G. Manzini, The nonconforming virtual element method. ESAIM: M2AN 50 (2014) 879–904. [Google Scholar]
  5. I. Babuška, C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for diffusion problems: 1-D analysis. CAMWA 37 (1999) 103–122. [Google Scholar]
  6. C. Baiocchi and F. Brezzi, Stabilization of unstable numerical methods. In: Problemi attuali dell’Analisi e della Fisica Matematica (1993). [Google Scholar]
  7. J. Banasiak and G.F. Roach, On mixed boundary value problems of Dirichlet oblique-derivative type in plane domains with piecewise differentiable boundary. J. Differ. Equ. 79 (1989) 111–131. [Google Scholar]
  8. G.R. Barrenechea, F. Jaillet, D. Paredes and F. Valentin, The multiscale hybrid mixed method in general polygonal meshes. Numer. Math. 125 (2020) 197–237. [Google Scholar]
  9. F. Bassi, L. Botti, S. Colombo and A. Rebay, Agglomeration based discontinuous Galerkin discretization of the Euler and Navier-Stokes equation. Comput. Fluids 61 (2012) 77–85. [Google Scholar]
  10. L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini and A. Russo, Basic principles of the virtual element method. M3AS 23 (2013) 199–214. [Google Scholar]
  11. L. Beirão da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method. M3AS 27 (2017) 2557–2594. [Google Scholar]
  12. S. Bertoluzza, Stabilization by multiscale decomposition. Appl. Math. Lett. 11 (1998) 129–134. [Google Scholar]
  13. S. Bertoluzza, Algebraic representation of dual scalar products and stabilization of saddle point problems. Preprint arXiv1906.01296(2019). [Google Scholar]
  14. S. Bertoluzza, C. Canuto and A. Tabacco, Stable discretizations of convection-diffusion problems via computable negative-order inner products. SIAM J. Numer. Anal. 38 (2000) 1034–1055. [Google Scholar]
  15. S. Bertoluzza, G. Manzini, M. Pennacchio and D. Prada, Stabilization of the nonconforming virtual element method. In preparation. [Google Scholar]
  16. S. Bertoluzza, I. Perugia and D. Prada, An h-p robust polygonal discontinuous Galerkin method with minus one stabilization. In preparation. [Google Scholar]
  17. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Vol. 44 of Springer Series in Computational Mathematics. Springer, Berlin-Heidelberg (2013). [Google Scholar]
  18. J.H. Bramble, J.E. Pasciak and P.S. Vassilevski, Computational scales of Sobolev norms with application to preconditioning. Math. Comput. 69 (2000) 463–480. [Google Scholar]
  19. S.C. Brenner and L.Y. Sung, Virtual element methods on meshes with small edges or faces. M3AS 28 (2018) 1291–1336. [Google Scholar]
  20. F. Brezzi, B. Cockburn, L.D. Marini and E. Süli, Stabilization mechanisms in discontinuous Galerkin finite element methods. MAME 195 (2006) 3293–3310. [Google Scholar]
  21. E. Burman and P. Hansbo, Edge stabilization for Galerkin approximations of convection–diffusion–reaction problems. CMAME 193 (2004) 1437–1453. [Google Scholar]
  22. A. Cangiani, Z. Dong, E.H. Georgoulis and P. Houston, hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. Springer Briefs in Mathematics. Springer, Cham (2017). [Google Scholar]
  23. L. Demkowicz and J. Gopalakrishnan, A class of discontinuous Petrov-Galerkin methods. Part II: optimal test functions. Numer. Methods Part. Differ. Equ. 27 (2011) 70–105. [Google Scholar]
  24. 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. Methods Appl. Math. 14 (2014) 461–472. [Google Scholar]
  25. R. Ewing, J. Wang and Y. Wang, A stabilized discontinuous finite element method for elliptic problems. Numer. Linear Algebra Appl. 10 (2003) 83–104. [Google Scholar]
  26. P. Ghysels, X. Li, F. Rouet, S. Williams and A. Napov, An efficient multicore implementation of a novel HSS-structured multifrontal solver using randomized sampling. SIAM J. Sci. Comput. 38 (2016) S358–S384. [Google Scholar]
  27. J. Guzmán and B. Rivière, Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations. J. Sci. Comput. 40 (2009) 273–280. [Google Scholar]
  28. P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection–diffusion–reaction problems. SIAM J. Numer. Anal. 39 (2002) 2133–2163. [Google Scholar]
  29. L. Mascotto, I. Perugia and A. Pichler, Non-conforming harmonic virtual element method: h- and p-versions. J. Sci. Comput. 77 (2018) 1874–1908. [Google Scholar]
  30. V. Maz’ya, Sobolev Spaces with Applications to Elliptic Partial Differential Equations. In: Vol. 342 of Grundlehren der mathematischen Wissenschaften. Springer, Berlin-Heidelberg (2011). [Google Scholar]
  31. P.A. Raviart and J.M. Thomas, Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comput. 31 (1977) 391–413. [Google Scholar]
  32. G. Rozza and K. Veroy, On the stability of reduced basis methods for Stokes equations in parametrized domains. CMAME 196 (2007) 1244–1260. [Google Scholar]
  33. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. In: Vol. 25 of Springer Series in Computational Mathematics, Springer, Berlin-Heidelberg (2006). [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