Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2503 - 2533
DOI https://doi.org/10.1051/m2an/2021062
Published online 29 October 2021
  1. R. Adams and J. Fournier, Sobolev spaces, 2nd edition. Elsevier (2003). [Google Scholar]
  2. I. Babuška, U. Banerjee and J.E. Osborn, Survey of meshless and generalized finite element methods: A unified approach. Acta Numer. 12 (2003) 1–125. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini and L.D. Marini, A. Russo, Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23 (2013) 199–214. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Beirao da Veiga, F. Brezzi and L.D. Marini, Virtual elements for linear elasticity problems. SIAM J. Numer. Anal. 51 (2013) 794–812. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Beirao da Veiga, K. Lipnikov and G. Manzini, The mimetic finite difference method for elliptic problems. Springer (2014). [Google Scholar]
  6. L. Beirao da Veiga, C. Lovadina and D. Mora, A virtual element method for elastic and inelastic problems on polytope meshes. Comput. Methods Appl. Mech. Eng. 295 (2015) 327–346. [CrossRef] [Google Scholar]
  7. L. Beirao da Veiga, C. Lovadina and G. Vacca, Divergence free virtual elements for the stokes problem on polygonal meshes. ESAIM: M2AN 51 (2017) 509–535. [CrossRef] [EDP Sciences] [Google Scholar]
  8. M. Botti, D.A. Di Pietro and P. Sochala, A hybrid high-order method for nonlinear elasticity. SIAM J. Numer. Anal. 2017 55 (2018) 2687–2717. [CrossRef] [Google Scholar]
  9. S. Brenner and R. Scott, The mathematical theory of finite element methods, 3rd edition. Springer (2008). [CrossRef] [Google Scholar]
  10. F. Chave, D.A. Di Pietro and L. Formaggia, A hybrid high-order method for darcy flows in fractured porous media. SIAM J. Sci. Comput. 40 (2018) 1063–1094. [Google Scholar]
  11. J.-S. Chen, M. Hillman and S.-W. Chi, Meshfree methods: Progress made after 20 years. J. Eng. Mech. 143 (2017) 04017001. [CrossRef] [Google Scholar]
  12. J. Coatléven, Principles of a network element method. J. Comput. Phys. 433 (2021) 110197. [CrossRef] [Google Scholar]
  13. D.A. Di Pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods. Springer (2012). [CrossRef] [Google Scholar]
  14. D.A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes. Comput. Methods Appl. Mech. Eng. 283 (2015) 1–21. [Google Scholar]
  15. D.A. Di Pietro and A. Ern, Hybrid high-order methods for variable-diffusion problems on general meshes. C.R. Acad. Sci. Paris, Ser. I 353 (2015) 31–34. [CrossRef] [Google Scholar]
  16. O. Diyankov, Uncertain grid method for numerical solution of PDES. Technical Report, NeurOK Software (2008). [Google Scholar]
  17. J. Droniou, R. Eymard, T. Gallouët, C. Guichard and R. Herbin, The gradient discretisation method. Springer (2018). [CrossRef] [Google Scholar]
  18. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. In: Techniques of scientific computiing, edited by P.G. Ciarlet and J.-L. Lions. Part III: Handbook of Numerical Analysis. North-Holland, Amsterdam (2000) 713–1020. [Google Scholar]
  19. R. Eymard, T. Gallouët and R. Herbin, Discretisation of heterogeneous and anisotropic diffusion problems on general nonconforming meshes sushi: a scheme using stabilisation and hybrid interfaces. IMA J. Num. Anal. 30 (2010) 1009–1043. [CrossRef] [Google Scholar]
  20. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman Publishing Inc, MA (1985). [Google Scholar]
  21. A. Katz and A. Jameson, Edge-based meshless methods for compressible viscous flow with applications to overset grids. In: Proceedings of the 38th Fluid Dynamics Conference and Exhibit. American Institute of Aeronautics and Astronautics (2008). [Google Scholar]
  22. A. Katz and A. Jameson, A meshless volume scheme. In: Proceedings of 19th AIAA Computational Fluid Dynamics, Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (2009) 2009–3534. [Google Scholar]
  23. E. Kwan Yu Chiu, Q. Wang, R. Hu and A. Jameson, A conservative mesh-free scheme and generalized framework for conservation laws. SIAM J. Sci. Comput. 34 (2012) 2896–2916. [Google Scholar]
  24. J.M. Melenk, On approximation in meshless methods. Springer Berlin Heidelberg, Berlin, Heidelberg (2005) 65–141. [Google Scholar]
  25. J.M. Melenk and I. Babuška, The partition of unity finite element method: Basic theory and applications. Comput. Methods Appl. Mech. Eng. 139 (1996) 289–314. [CrossRef] [Google Scholar]
  26. E.M. Stein, Singular integrals and differentiability properties of functions. Princeton University Press (1970). [Google Scholar]
  27. N. Trask, P. Bochev and M. Perego, A conservative, consistent, and scalable mesh-free mimetic method. J. Comput. Phys. 409 (2020) 109–187. [Google Scholar]
  28. N. Trask, M. Perego and P. Bochev, A high-order staggered meshless method for elliptic problems. SIAM J. Sci. Comput. 39 (2017) 479–502. [Google Scholar]
  29. G. Vacca and L. Beirao da Veiga, Virtual element methods for parabolic problems on polygonal meshes. Numer. Methods Partial Differ. Equ. 31 (2015) 2110–2134. [CrossRef] [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