Open Access
| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2491 - 2514 | |
| DOI | https://doi.org/10.1051/m2an/2025054 | |
| Published online | 17 September 2025 | |
- P. Aluffi, Algebra: Chapter 0. Vol. 104. American Mathematical Society (2021). [Google Scholar]
- A. Armiti-Juber and C. Rohde, Existence of weak solutions for a nonlocal pseudo-parabolic model for Brinkman two-phase flow in asymptotically flat porous media. J. Math. Anal. App. 477 (2019) 592–612. [Google Scholar]
- D.N. Arnold, Finite Element Exterior Calculus. SIAM (2018). [Google Scholar]
- D.N. Arnold, R.S. Falk and R. Winther, Differential complexes and stability of finite element methods II: the elasticity complex, in Compatible Spatial Discretizations. Springer (2006) 47–67. [Google Scholar]
- D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [Google Scholar]
- D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Am. Math. Soc. 47 (2010) 281–354. [Google Scholar]
- D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Vol. 44. Springer (2013). [Google Scholar]
- W.M. Boon and J.M. Nordbotten, Mixed-dimensional poromechanical models of fractured porous media. Acta Mech. 234 (2023) 1121–1168. [Google Scholar]
- W.M. Boon, J.M. Nordbotten and J.E. Vatne, Functional analysis and exterior calculus on mixed-dimensional geometries. Annali di Matematica Pura ed Applicata (1923-) 200 (2021) 757–789. [Google Scholar]
- W.M. Boon, D.F. Holmen, J.M. Nordbotten and J.E. Vatne, The Hodge-Laplacian on the Čech-de Rham complex governs coupled problems. J. Math. Anal. App. 551 (2025) 129692. [Google Scholar]
- R. Bott and L.W. Tu, Differential Forms in Algebraic Topology. Vol. 82. Springer (1982). [Google Scholar]
- J.R. Brauer and B.S. Brown, Mixed-dimensional finite-element models of electromagnetic coupling and shielding. IEEE Trans. Electromagn. Compat. 35 (1993) 235–241. [Google Scholar]
- A. Buffa and S.H. Christiansen, The electric field integral equation on Lipschitz screens: definitions and numerical approximation. Numer. Math. 94 (2003) 229–267. [Google Scholar]
- A. Chambolle, An approximation result for special functions with bounded deformation. Journal de mathématiques pures et appliquées 83 (2004) 929–954. [Google Scholar]
- O. Coussy, Poromechanics. John Wiley & Sons (2004). [Google Scholar]
- C. D’Angelo and A. Quarteroni, On the coupling of 1d and 3d diffusion-reaction equations: application to tissue perfusion problems. Math. Models Methods Appl. Sci. 18 (2008) 1481–1504. [CrossRef] [MathSciNet] [Google Scholar]
- G.A. Deschamps, Electromagnetics and differential forms. Proc. IEEE 69 (1981) 676–696. [Google Scholar]
- R.S. Falk and M. Neilan, Stokes complexes and the construction of stable finite elements with pointwise mass conservation. SIAM J. Numer. Anal. 51 (2013) 1308–1326. [CrossRef] [MathSciNet] [Google Scholar]
- R.S. Falk and R. Winther, Double complexes and local cochain projections. Numer. Methods Part. Differ. Equ. 31 (2015) 541–551. [Google Scholar]
- M.W. Hirsch, Differential Topology. Vol. 33. Springer Science & Business Media (2012). [Google Scholar]
- N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM (1988). [Google Scholar]
- T. Köppl, E. Vidotto, B. Wohlmuth and P. Zunino, Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions. Math. Models Methods Appl. Sci. 28 (2018) 953–978. [Google Scholar]
- F. Laurino and P. Zunino, Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction. ESAIM: Math. Model. Numer. Anal. 53 (2019) 2047–2080. [Google Scholar]
- J.M. Lee, Smooth Manifolds. Springer (2012). [Google Scholar]
- M.W. Licht, Complexes of discrete distributional differential forms and their homology theory. Found. Comput. Math. 17 (2017) 1085–1122. [Google Scholar]
- T. Linse, P. Hennig, M. K¨astner and R. de Borst, A convergence study of phase-field models for brittle fracture. Eng. Fract. Mech. 184 (2017) 307–318. [Google Scholar]
- F. List, K. Kumar, I.S. Pop and F.A. Radu, Rigorous upscaling of unsaturated flow in fractured porous media. SIAM J. Math. Anal. 52 (2020) 239–276. [Google Scholar]
- E. Oterkus, S. Oterkus and E. Madenci, Peridynamic Modeling, Numerical Techniques, and Applications. Elsevier (2021). [Google Scholar]
- D. Pauly, Solution theory, variational formulations, and functional a posteriori error estimates for general first order systems with applications to electro-magneto-statics and more. Numer. Funct. Anal. Optim. 41 (2020) 16–112. [Google Scholar]
- D. Pauly and W. Zulehner, The elasticity complex: compact embeddings and regular decompositions. Appl. Anal. 102 (2023) 4393–4421. [Google Scholar]
- S. Repin, A Posteriori Estimates for Partial Differential Equations. Walter de Gruyter (2008). [Google Scholar]
- T. Richter, Fluid-Structure Interactions: Models, Analysis and Finite Elements. Vol. 118. Springer (2017). [Google Scholar]
- R. Temam and A. Miranville, Mathematical Modeling in Continuum Mechanics. Cambridge University Press (2005). [Google Scholar]
- C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics. Springer (2004). [Google Scholar]
- Y.C. Yortsos, A theoretical analysis of vertical flow equilibrium. Transp. Porous Media 18 (1995) 107–129. [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.