Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
---|---|---|
Page(s) | 1921 - 1952 | |
DOI | https://doi.org/10.1051/m2an/2023033 | |
Published online | 03 July 2023 |
- E. Ahmed, F. Radu and J. Nordbotten, Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot’s consolidation model. Comput. Methods Appl. Mech. Eng. 347 (2019) 264–294. [CrossRef] [Google Scholar]
- E.C. Aifantis, On the problem of diffusion in solids. Acta Mech. 37 (1980) 265–296. [CrossRef] [MathSciNet] [Google Scholar]
- M. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M.E. Rognes and G. Wells, The FEniCS project version 1.5. Arch. Numer. Soft. 3 (2015). [Google Scholar]
- M. Bai, D. Elsworth and J.-C. Roegiers, Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs. Water Resour. Res. 29 (1993) 1621–1633. [CrossRef] [Google Scholar]
- G.I. Barenblatt, On certain boundary-value problems for the equations of seepage of a liquid in fissured rocks. J. Appl. Math. Mech. 27 (1963) 513–518. [CrossRef] [Google Scholar]
- G.I. Barenblatt, IuP Zheltov and I.N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissued rocks (strata). J. Appl. Math. Mech. 24 (1960) 1286–1303. [CrossRef] [Google Scholar]
- M. Bendahmane, R. Bürger and R. Ruiz-Baier, A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology. Numer. Methods Partial Differ. Equ. 26 (2010) 1377–1404. [CrossRef] [Google Scholar]
- M. Biot, General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941) 155–164. [Google Scholar]
- M. Biot, Theory of elasticity and consolidation for a porous anisotropic media. J. Appl. Phys. 26 (1955) 182–185. [CrossRef] [MathSciNet] [Google Scholar]
- S. Budday, R. Nay, R. de Rooij, P. Steinmann, T. Wyrobek, T. Ovaert and E. Kuhl, Mechanical properties of gray and white matter brain tissue by indentation. J. Mech. Behav. Biomed. Mater. 46 (2015) 318–330. [CrossRef] [Google Scholar]
- J.B. Conway, A Course in Functional Analysis, 2nd ed., Springer-Verlag, New York, NY (1997). [Google Scholar]
- C. Daversin-Catty, V. Vinje, K.-A. Mardal and M.E. Rognes, The mechanisms behind perivascular fluid flow. Plos One 15 (2020) e0244442. [CrossRef] [PubMed] [Google Scholar]
- W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [Google Scholar]
- A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Springer-Verlag (2004). [CrossRef] [Google Scholar]
- A. Ern and S. Meunier, A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems. Math. Model. Numer. Anal. 43 (2009) 353–375. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- L. Evans, Partial Differential Equations. American Mathematical Society, Providence, R.I. (2010). [Google Scholar]
- B. Fischl, Freesurfer. Neuroimage 62 (2012) 774–781. [CrossRef] [PubMed] [Google Scholar]
- L. Guo, J. Vardakis, T. Lassila, M. Mitolo, N. Ravikumar, D. Chou, M. Lange, A. Sarrami-Foroushani, B. Tully, Z. Taylor, S. Varma, A. Venneri, A. Frangi and Y. Ventikos, Subject-specific multi-poroelastic model for exploring the risk factors associated with the early stages of Alzheimer’s disease. Interface Focus 8 (2018) 1–15. [Google Scholar]
- L. Guo, Z. Li, J. Lyu, Y. Mei, J. Vardakis, D. Chen, C. Han, X. Lou and Y. Ventikos, On the validation of a multiple-network poroelastic model using arterial spin labeling mri data. Frontiers in Comput. Neurosci. 13 (2019) 60. [CrossRef] [Google Scholar]
- M.Y. Khaled, D.E. Beskos and E.C. Aifantis, On the theory of consolidation with double porosity. III. A finite-element formulation. Int. J. Numer. Anal. Meth. Geomech. 8 (1984) 101–123. [CrossRef] [Google Scholar]
- A. Khan and D. Silvester, Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity. IMA J. Numer. Anal. 41 (2020) 2000–2025. [Google Scholar]
- K. Kuman, S. Kyas, J. Nordbotten and S. Repin, Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. Comput. Math. Appl. 91 (2021) 122–149. [CrossRef] [MathSciNet] [Google Scholar]
- J.J. Lee, E. Piersanti, K.-A. Mardal and M.E. Rognes, A mixed finite element method for nearly incompressible multiple-network poroelasticity. SIAM J. Sci. Comput. 41 (2019) A722–A747. [Google Scholar]
- Y. Li and L. Zikatanov, Residual-based a posteriori error estimates of mixed methods for a three-field Biot’s consolidation model. Preprint Preprint arXiv:1911.08692 (2019). [Google Scholar]
- Z. Lotfian and M.V. Sivaselvan, Mixed finite element formulation for dynamics of porous media. Int. J. Numer. Methods Eng. 115 (2018) 141–171. [CrossRef] [Google Scholar]
- K.-A. Mardal, M.E. Rognes, T.B. Thompson and L. Magnus Valnes, Mathematical Modeling of the Human Brain: From Magnetic Resonance Images to Finite Element Simulation. Springer (2021). [Google Scholar]
- J. Nordbotten, T. Rahman, S.I. Repin and J. Valdman, A posteriori error estimates for approximate solutions of the Barenblatt-Biot poroelastic model. Comput. Methods Appl. Math. 10 (2010) 302–314. [CrossRef] [MathSciNet] [Google Scholar]
- Á. Plaza and M.-C. Rivara, Mesh refinement based on the 8-tetrahedra longest-edge partition, in IMR, Citeseer (2003) 67–78. [Google Scholar]
- O. Ricardo and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity. SIAM J. Numer Anal. 54 (2016) 2951–2973. [CrossRef] [MathSciNet] [Google Scholar]
- R. Riedlbeck, D. Di Pietro, A. Ern, S. Granet and K. Kazymyrenko, Stress and flux reconstructions in Biot’s poro-elasticity problem with application to a posteriori error analysis. Comput. Math. Appl. 73 (2017) 1593–1610. [CrossRef] [MathSciNet] [Google Scholar]
- C. Rodrigo, X. Hu, P. Ohm, J.H. Adler, F.J. Gaspar and L.T. Zikatanov, New stabilized discretizations for poroelasticity and the Stoke’s equations. Comput. Methods Appl. Mech. Eng. 341 (2018) 467–484. [CrossRef] [Google Scholar]
- R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl. 24 (2000) 310–340. [CrossRef] [MathSciNet] [Google Scholar]
- R.E. Showalter and B. Momken, Single-phase flow in composite poroelastic media. Math. Methods Appl. Sci. 25 (2002) 115–139. [CrossRef] [MathSciNet] [Google Scholar]
- G. Söderlind, Automatic control and adaptive time-stepping. Numer. Algorithms 31 (2002) 281–310. [CrossRef] [MathSciNet] [Google Scholar]
- K. Terzaghi, Theoretical Soil Mechanics. Wiley (1943). [CrossRef] [Google Scholar]
- B. Tully and Y. Ventikos, Cerebral water transport using multiple-network poroelastic theory: application to normal pressure hydrocephalus. J. Fluid. Mech. 667 (2011) 188–215. [Google Scholar]
- J. Vardakis, D. Chou, B. Tully, C. Hung, T. Lee, P.-H. Tsui and Y. Ventikos, Investigating cerebral oedema using poroelasticity. Med. Eng. Phys. 38 (2016) 48–57. [CrossRef] [Google Scholar]
- V. Vinje, A. Eklund, K.-A. Mardal, M.E. Rognes anb K.-H. Støverud, Intracranial pressure elevation alters CSF clearance pathways. Fluids Barriers CNS 17 (2020) 1–19. [CrossRef] [PubMed] [Google Scholar]
- R.K. Wilson and E.C. Aifantis, On the theory of consolidation with double porosity. Int. J. Eng. Sci. 20 (1982) 1009–1035. [CrossRef] [Google Scholar]
- J. Young, B. Riviere, C. Cox and K. Uray, A mathematical model of intestinal edema formation. Math. Med. Bio. 31 (2014) 1189–1210. [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.