Free Access
Issue |
ESAIM: M2AN
Volume 48, Number 5, September-October 2014
|
|
---|---|---|
Page(s) | 1331 - 1349 | |
DOI | https://doi.org/10.1051/m2an/2013141 | |
Published online | 13 August 2014 |
- H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311–341. [CrossRef] [MathSciNet] [Google Scholar]
- L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives. Pacific J. Math. 16 (1966) 1–3. [Google Scholar]
- H. Berninger, Domain Decomposition Methods for Elliptic Problems with Jumping Nonlinearities and Application to the Richards Equation. Ph.D. thesis. Freie Universität Berlin (2007). [Google Scholar]
- H. Berninger, Non-overlapping domain decomposition for the Richards equation via superposition operators. Vol. 70 of Lect. Notes Comput. Sci. Eng. Springer, Berlin (2009) 169–176. [Google Scholar]
- H. Berninger, R. Kornhuber and O. Sander, On nonlinear Dirichlet-Neumann algorithms for jumping nonlinearities. Domain decomposition methods in science and engineering XVI. Vol. 55 of Lect. Notes Comput. Sci. Eng. Springer, Berlin (2007) 489–496. [Google Scholar]
- H. Berninger, R. Kornhuber and O. Sander, Fast and robust numerical solution of the Richards equation in homogeneous soil. SIAM J. Numer. Anal. 49 (2011) 2576–2597. [CrossRef] [Google Scholar]
- A. Bourlioux and A.J. Majda, An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion. Combust. Theory Model. 4 (2000) 189–210. [CrossRef] [MathSciNet] [Google Scholar]
- R.H. Brooks and A.T. Corey, Hydraulic properties of porous media. Hydrol. Pap. 4, Colo. State Univ., Fort Collins (1964). [Google Scholar]
- N.T. Burdine, Relative permeability calculations from pore-size distribution data. Petr. Trans. Am. Inst. Mining Metall. Eng. 198 (1953) 71–77. [Google Scholar]
- C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM: M2AN 33 (1999) 1187–1202. [CrossRef] [EDP Sciences] [Google Scholar]
- C. Carstensen and R. Verfürth, Edge residuals dominate a posteriori error estimates for low order finite element methods. SIAM J. Numer. Anal. 36 (1999) 1571–1587. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Dennis Jr. and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM Classics Appl. Math. (1996). [Google Scholar]
- W. E and B. Engquist, The heterogeneous multiscale methods. Commun. Math. Sci. 1 (2003) 87–132. [CrossRef] [MathSciNet] [Google Scholar]
- A. Gloria, An analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies. SIAM Multiscale Model. Simul. 5 (2006) 996–1043. [Google Scholar]
- P. Henning, Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems. Netw. Heterog. Media 7 (2012) 503–524. [CrossRef] [MathSciNet] [Google Scholar]
- P. Henning and M. Ohlberger, The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. Netw. Heterog. Media 5 (2010) 711–744. [CrossRef] [MathSciNet] [Google Scholar]
- P. Henning and M. Ohlberger, A Note on Homogenization of Advection-Diffusion Problems with Large Expected Drift. Z. Anal. Anwend. 30 (2011) 319–339. [CrossRef] [MathSciNet] [Google Scholar]
- P. Henning and M. Ohlberger, Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems. Preprint 01/11 – N, to appear in DCDS-S, special issue on Numerical Methods based on Homogenization and Two-Scale Convergence (2011). [Google Scholar]
- P. Henning and D. Peterseim, Oversampling for the Multiscale Finite Element Method. SIAM Multiscale Model. Simul. 12 (2013) 1149–1175. [CrossRef] [MathSciNet] [Google Scholar]
- T. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169–189. [CrossRef] [MathSciNet] [Google Scholar]
- T.J.R. Hughes, G.R. Feijóo, L. Mazzei and J.-B. Quincy, The variational multiscale method – a paradigm for computational mechanics. Comput. Methods Appl. Mech. Engrg. 166 (1998) 3–24. [Google Scholar]
- T.J.R. Hughes and G. Sangalli, Variational multiscale analysis: the fine-scale Green?s function, projection, optimization, localization, and stabilized methods. SIAM J. Numer. Anal. 45 (2007) 539–557. [Google Scholar]
- W.R. Gardner, Some steady state solutions of unsaturated moisture ßow equations with application to evaporation from a water table. Soil Sci. 85 (1958) 228–232. [Google Scholar]
- M.T. van Genuchten, A closedform equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44 (1980) 892–898. [Google Scholar]
- J. Karátson, Characterizing Mesh Independent Quadratic Convergence of Newton’s Method for a Class of Elliptic Problems. J. Math. Anal. 44 (2012) 1279–1303. [CrossRef] [MathSciNet] [Google Scholar]
- C.T. Kelley, Iterative methods for linear and nonlinear equations. In vol. 16. SIAM Frontiers in Applied Mathematics (1996). [Google Scholar]
- M.G. Larson and A. Målqvist, Adaptive variational multiscale methods based on a posteriori error estimation: energy norm estimates for elliptic problems. Comput. Methods Appl. Mech. Engrg. 196 (2007) 2313–2324. [CrossRef] [MathSciNet] [Google Scholar]
- M.G. Larson and A. Målqvist, An adaptive variational multiscale method for convection-diffusion problems. Commun. Numer. Methods Engrg. 25 (2009) 65–79. [CrossRef] [Google Scholar]
- M.G. Larson and A. Målqvist, A mixed adaptive variational multiscale method with applications in oil reservoir simulation. Math. Models Methods Appl. Sci. 19 (2009) 1017–1042. [CrossRef] [Google Scholar]
- A. Målqvist, Multiscale methods for elliptic problems. Multiscale Model. Simul. 9 (2011) 1064–1086. [CrossRef] [Google Scholar]
- A. M alqvist and D. Peterseim, Localization of Elliptic Multiscale Problems. To appear in Math. Comput. (2011). Preprint arXiv:1110.0692v4. [Google Scholar]
- Y. Mualem, A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media. Water Resour. Res. 12 (1976) 513–522. [Google Scholar]
- J.M. Nordbotten, Adaptive variational multiscale methods for multiphase flow in porous media. SIAM Multiscale Model. Simul. 7 (2008) 1455–1473. [CrossRef] [Google Scholar]
- D. Peterseim, Robustness of Finite Element Simulations in Densely Packed Random Particle Composites. Netw. Heterog. Media 7 (2012) 113–126. [CrossRef] [MathSciNet] [Google Scholar]
- D. Peterseim and S.A. Sauter, Finite Elements for Elliptic Problems with Highly Varying, Non-Periodic Diffusion Matrix. SIAM Multiscale Model. Simul. 10 (2012) 665–695. [CrossRef] [Google Scholar]
- M. Růžička, Nichtlineare Funktionalanalysis. Oxford Mathematical Monographs. Springer-Verlag, Berlin, Heidelberg, New York (2004). [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.