Free Access
Issue |
ESAIM: M2AN
Volume 42, Number 3, May-June 2008
|
|
---|---|---|
Page(s) | 375 - 410 | |
DOI | https://doi.org/10.1051/m2an:2008009 | |
Published online | 03 April 2008 |
- Y. Achdou and C. Bernardi, Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable. C. R. Acad. Sci. Paris Sér. I 333 (2001) 693–698. [Google Scholar]
- Y. Achdou, C. Bernardi and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy's equations. Numer. Math. 96 (2003) 17–42. [CrossRef] [MathSciNet] [Google Scholar]
- R.A. Adams, Sobolev Spaces. Academic Press (1975). [Google Scholar]
- S. Antontsev, A.V. Kazhikhov and V.N. Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids [English transl.], Studies in Mathematics and its Applications 22. North-Holland (1990). [Google Scholar]
- F. Ben Belgacem, The Mortar finite element method with Lagrangian multiplier. Numer. Math. 84 (1999) 173–197. [CrossRef] [MathSciNet] [Google Scholar]
- C. Bernardi and G. Raugel, Analysis of some finite elements for the Stokes problem. Math. Comput. 44 (1985) 71–79. [CrossRef] [Google Scholar]
- C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar XI, H. Brezis and J.-L. Lions Eds., Pitman (1994) 13–51. [Google Scholar]
- C. Bernardi, B. Métivet and R. Verfürth, Analyse numérique d'indicateurs d'erreur, in Maillage et adaptation, Chap. 8, P.-L. George Ed., Hermès (2001) 251–278. [Google Scholar]
- C. Bernardi, Y. Maday and F. Rapetti, Discrétisations variationnelles de problèmes aux limites elliptiques, Collection Mathématiques et Applications 45. Springer-Verlag (2004). [Google Scholar]
- C. Bernardi, F. Hecht and O. Pironneau, Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: M2AN 39 (2005) 7–35. [CrossRef] [EDP Sciences] [Google Scholar]
- C. Bernardi, Y. Maday and F. Rapetti, Basics and some applications of the mortar element method. GAMM – Gesellschaft für Angewandte Mathematik und Mechanik 28 (2005) 97–123. [Google Scholar]
- C. Bernardi, F. Hecht and Z. Mghazli, Mortar finite element discretization for the flow in a non homogeneous porous medium. Comput. Methods Appl. Mech. Engrg. 196 (2007) 1554–1573. [CrossRef] [MathSciNet] [Google Scholar]
- J. Boland and R. Nicolaides, Stability of finite elements under divergence constraints. SIAM J. Numer. Anal. 20 (1983) 722–731. [CrossRef] [MathSciNet] [Google Scholar]
- D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431–2444. [CrossRef] [MathSciNet] [Google Scholar]
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics 15. Springer-Verlag (1991). [Google Scholar]
- E. Burman and P. Hansbo, A unified stabilized method for Stokes' and Darcy's equations. J. Comput. Applied Math. 198 (2007) 35–51. [Google Scholar]
- D.-G. Calugaru, Modélisation et simulation numérique du transport de radon dans un milieu poreux fissuré ou fracturé. Problème direct et problèmes inverses comme outils d'aide à la prédiction sismique. Ph.D. thesis, Université de Franche-Comté, Besançon, France (2002). [Google Scholar]
- C. Carstensen and J. Hu, A unifying theory of a posteriori error control for nonconforming finite element methods. Numer. Math. 107 (2007) 473–502. [CrossRef] [MathSciNet] [Google Scholar]
- M. Dauge, Neumann and mixed problems on curvilinear polyhedra. Integr. Equat. Oper. Th. 15 (1992) 227–261. [Google Scholar]
- G. de Marsily, Quantitative Hydrology. Groundwater Hydrology for Engineers. Academic Press, New York (1986). [Google Scholar]
- M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43 (2002) 57–74. [CrossRef] [MathSciNet] [Google Scholar]
- M. Fortin, Old and new elements for incompressible flows. Internat. J. Numer. Methods Fluids 1 (1981) 347–364. [CrossRef] [MathSciNet] [Google Scholar]
- J. Galvis and M. Sarkis, Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. (Submitted). [Google Scholar]
- V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer Series in Computational Mathematics 5. Springer-Verlag (1986). [Google Scholar]
- V. Girault, R. Glowinski and H. López, A domain decomposition and mixed method for a linear parabolic boundary value problem. IMA J. Numer. Anal. 24 (2004) 491–520. [CrossRef] [MathSciNet] [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains . Pitman (1985). [Google Scholar]
- F. Hecht and O. Pironneau, FreeFem++, see www.freefem.org. [Google Scholar]
- W.J. Layton, F. Schieweck and I. Yotov, Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40 (2002) 2195–2218. [CrossRef] [MathSciNet] [Google Scholar]
- R. Lewandowski, Analyse mathématique et océanographie, Collection Recherches en Mathématiques Appliquées. Masson (1997). [Google Scholar]
- J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod (1968). [Google Scholar]
- J.-C. Nédélec, Mixed finite elements in . Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
- M. Orlt and A.-M. Sändig, Regularity of viscous Navier-Stokes flows in nonsmooth domains, in Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge and S. Nicaise Eds., Lect. Notes Pure Appl. Math. 167, Dekker (1995) 185–201. [Google Scholar]
- K.R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solids. Math. Models Methods Appl. Sci. 17 (2007) 215–252. [CrossRef] [MathSciNet] [Google Scholar]
- P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lect. Notes Math. 606, Springer (1977) 292–315. [Google Scholar]
- J.M. Urquiza, D. N'Dri, A. Garon and M.C. Delfour, Coupling Stokes and Darcy equations. Applied Numer. Math. (2007) (in press). [Google Scholar]
- R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques . Wiley & Teubner (1996). [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.