Open Access
Volume 56, Number 2, March-April 2022
Page(s) 505 - 528
Published online 24 February 2022
  1. O. Bauchau and J. Craig, Structural Analysis: With Applications to Aerospace Structures. Solid Mechanics and Its Applications. Springer, Netherlands (2009). [Google Scholar]
  2. L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini and A. Russo, Basic principles of virtual element methods. Math. Mod. Meth. Appl. Sci. 23 (2013) 199–214. [CrossRef] [Google Scholar]
  3. L. Beirão da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method. Math. Mod. Meth. Appl. Sci. 27 (2017) 2557–2594. [CrossRef] [Google Scholar]
  4. M. Ben-Artzi and P.G. LeFloch, Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds. Ann. Inst. Henri Poincaré C, Anal. Non Linéaire 24 (2007) 989–1008. [CrossRef] [Google Scholar]
  5. I. Berre, F. Doster and E. Keilegavle, Flow in fractured porous media: A review of conceptual models and discretization approaches. Transp. Porous Media 130 (2019) 215–236. [CrossRef] [MathSciNet] [Google Scholar]
  6. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics. Vol 15, Springer, Berlin, Heidelberg (2013). [CrossRef] [Google Scholar]
  7. A. Bressan, S. Canic, M. Garavello, M. Herty and B. Piccoli, Flows on networks: Recent results and perspectives. EMS Surv. Math. Sci. 1 (2014) 47–111. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi, J. Douglas and D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  9. 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]
  10. P. Ciarlet, Mathematical Elasticity: Volume II: Theory of Plates. Elsevier (1997). [Google Scholar]
  11. P. Ciarlet, Theory of Shells. Elsevier (2000). [Google Scholar]
  12. B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47 (2009) 1319–1365. [Google Scholar]
  13. B. Cockburn, J. Guzmán and H. Wang, Superconvergent discontinuous Galerkin methods for second-order elliptic problems. Math. Comput. 78 (2009) 1–24. [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. Meth. Appl. Mech. Eng. 283 (2015) 1–21. [CrossRef] [Google Scholar]
  15. G. Dziuk and C.M. Elliott, Finite element methods for surface PDEs. Acta Numer. 22 (2013) 289–396. [Google Scholar]
  16. V. Eremeyev, Two- and three-dimensional elastic networks with rigid junctions: Modeling within the theory of micropolar shells and solids. Acta Mech. 230 (2019) 3875–3887. [CrossRef] [MathSciNet] [Google Scholar]
  17. L.C. Evans, Partial Differential Equations. American Mathematical Society (1998). [Google Scholar]
  18. I. Fatt, The network model of porous media. Trans. AIME 207 (1956) 144–181. [CrossRef] [Google Scholar]
  19. U.S. Fjordholm, M. Musch and N.H. Risebro, Well-posedness theory for nonlinear scalar conservation laws on networks. Preprint arXiv:2102.06400 (2021). [Google Scholar]
  20. M. Garavello, A review of conservation laws on networks. Netw. Heterog. Media 5 (2010) 565. [CrossRef] [MathSciNet] [Google Scholar]
  21. F. Hédin, G. Pichot and A. Ern, A hybrid high-order method for flow simulations in discrete fracture networks. In: ENUMATH – European Numerical Mathematics and Advanced Applications Conference 2019. Springer Professional (2019). [Google Scholar]
  22. C. Heussinger, On the elasticity of stiff polymer networks. Ph.D. thesis, Ludwig-Maximilians-Universität München (2007). [Google Scholar]
  23. C. Heussinger and E. Frey, Stiff polymers, foams, and fiber networks. Phys. Rev. Lett. 96 (2006) 017802. [CrossRef] [PubMed] [Google Scholar]
  24. C. Heussinger, B. Schaefer and E. Frey, Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E 76 (2007) 031906. [CrossRef] [PubMed] [Google Scholar]
  25. R.V.S. Kanda and M. Simons, An elastic plate model for interseismic deformation in subduction zones. J. Geophys. Res.: Solid Earth 115 (2010) 19. [Google Scholar]
  26. J.E. Lagnese and G. Leugering, Modelling of dynamic networks of thin elastic plates. Math. Methods Appl. Sci. 16 (1993) 379–407. [CrossRef] [MathSciNet] [Google Scholar]
  27. H. Le Dret, Folded plates revisited. Comput. Mech. 5 (1989) 345–365. [CrossRef] [Google Scholar]
  28. O. Lieleg, M.M.A.E. Claessens, C. Heussinger, E. Frey and A.R. Bausch, Mechanics of bundled semiflexible polymer networks, Phys. Rev. Lett. 99 (2007) 088102. [CrossRef] [PubMed] [Google Scholar]
  29. E. Marušić-Paloka, Rigorous justification of the Kirchhoff law for junction of thin pipes filled with viscous fluid. Asymptot. Anal. 33 (2003) 51–66. [MathSciNet] [Google Scholar]
  30. E. Marušić-Paloka, Mathematical modeling of junctions in fluid mechanics via two-scale convergence. J. Math. Anal. Appl. 480 (2019) 1–25. [Google Scholar]
  31. I. Perugia, P. Pietra and A. Russo, A plane wave virtual element method for the helmholtz problem. ESAIM: M2AN 50 (2016) 783–808. [CrossRef] [EDP Sciences] [Google Scholar]
  32. W. Qiu, M. Solano and P. Vega, A high order HDG method for curved-interface problems via approximations from straight triangulations. J. Sci. Comput. 69 (2016) 1384–1407. [CrossRef] [MathSciNet] [Google Scholar]
  33. P.A. Raviart and J.M. Thomas, A mixed finite element method for 2-nd order elliptic problems. In: Mathematical Aspects of Finite Element Methods, edited by I. Galligani and E. Magenes. Springer Berlin Heidelberg, Berlin, Heidelberg (1977) 292–315. [CrossRef] [Google Scholar]
  34. 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]
  35. N. Ray, A. Rupp, R. Schulz and P. Knabner, Old and new approaches predicting the diffusion in porous media. Transp. Porous Media 124 (2018) 803–824. [CrossRef] [Google Scholar]
  36. V. Reichenberger, H. Jakobs, P. Bastian and R. Helmig, A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv. Water Res. 29 (2006) 1020–1036. [CrossRef] [Google Scholar]
  37. F. Rüffler, V. Mehrmann and F. Hante, Optimal model switching for gas flow in pipe networks. Netw. Heterog. Media 13 (2018) 641. [CrossRef] [MathSciNet] [Google Scholar]
  38. A. Rupp and G. Kanschat, HyperHDG: Hybrid discontinuous Galerkin methods for PDEs on hypergraphs (2021). Published online. [Google Scholar]
  39. R. Schulz, N. Ray, S. Zech, A. Rupp and P. Knabner, Beyond Kozeny–Carman: Predicting the permeability in porous media. Transp. Porous Media 130 (2019) 487–512. [CrossRef] [MathSciNet] [Google Scholar]
  40. K. Weishaupt, V. Joekar-Niasar and R. Helmig, An efficient coupling of free flow and porous media flow using the pore-network modeling approach. J. Comput. Phys. 1 (2019) 100011. [MathSciNet] [Google Scholar]

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