Open Access
Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
---|---|---|
Page(s) | 505 - 528 | |
DOI | https://doi.org/10.1051/m2an/2022011 | |
Published online | 24 February 2022 |
- O. Bauchau and J. Craig, Structural Analysis: With Applications to Aerospace Structures. Solid Mechanics and Its Applications. Springer, Netherlands (2009). [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. Mod. Meth. Appl. Sci. 23 (2013) 199–214. [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. Ciarlet, Mathematical Elasticity: Volume II: Theory of Plates. Elsevier (1997). [Google Scholar]
- P. Ciarlet, Theory of Shells. Elsevier (2000). [Google Scholar]
- 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]
- 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]
- 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]
- G. Dziuk and C.M. Elliott, Finite element methods for surface PDEs. Acta Numer. 22 (2013) 289–396. [Google Scholar]
- 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]
- L.C. Evans, Partial Differential Equations. American Mathematical Society (1998). [Google Scholar]
- I. Fatt, The network model of porous media. Trans. AIME 207 (1956) 144–181. [CrossRef] [Google Scholar]
- 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]
- M. Garavello, A review of conservation laws on networks. Netw. Heterog. Media 5 (2010) 565. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- C. Heussinger, On the elasticity of stiff polymer networks. Ph.D. thesis, Ludwig-Maximilians-Universität München (2007). [Google Scholar]
- C. Heussinger and E. Frey, Stiff polymers, foams, and fiber networks. Phys. Rev. Lett. 96 (2006) 017802. [CrossRef] [PubMed] [Google Scholar]
- C. Heussinger, B. Schaefer and E. Frey, Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E 76 (2007) 031906. [CrossRef] [PubMed] [Google Scholar]
- 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]
- 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]
- H. Le Dret, Folded plates revisited. Comput. Mech. 5 (1989) 345–365. [CrossRef] [Google Scholar]
- 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]
- 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]
- E. Marušić-Paloka, Mathematical modeling of junctions in fluid mechanics via two-scale convergence. J. Math. Anal. Appl. 480 (2019) 1–25. [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Rupp and G. Kanschat, HyperHDG: Hybrid discontinuous Galerkin methods for PDEs on hypergraphs (2021). Published online. [Google Scholar]
- 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]
- 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]
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.