Abstract
The exchange of ground- and surface water plays a crucial role in a variety of practically relevant processes ranging from flood protection measures to preservation of ecosystem health in natural and human-impacted water resources systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
H.W. Alt and S. Luckhaus. Quasilinear elliptic–parabolic differential equations. Math. Z., 183:311–341, 1983.
P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A generic interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE. Computing, 82(2–3):121–138, 2008.
P. Bastian, G. Buse, and O. Sander. Infrastructure for the coupling of Dune grids. In Proc. of ENUMATH 2009, pages 107–114. Springer, 2010.
H. Berninger, R. Kornhuber, and O. Sander. Fast and robust numerical solution of the Richards equation in homogeneous soil. Technical Report A /01/2010, FU Berlin, 2010. submitted to SIAM J. Numer. Anal.
F. Brezzi and G. Gilardi. Functional spaces. In H. Kardestuncer and D.H. Norrie, editors, Finite Element Handbook, chapter 2 (part 1), pages 1.29–1.75. Springer, 1987.
R.J. Brooks and A.T. Corey. Hydraulic properties of porous media. Technical Report Hydrology Paper No. 3, Colorado State University, 1964.
N.T. Burdine. Relative permeability calculations from pore-size distribution data. Petr. Trans., Am. Inst. Mining Metall. Eng., 198:71–77, 1953.
C. Dawson. Analysis of discontinuous finite element methods for ground water/surface water coupling. SIAM J. Numer. Anal., 44(4):1375–1404, 2006.
C. Dawson. A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow. Comput. Geosci, 12:451–472, 2008.
S. Deparis, M. Discacciati, G. Fourestey, and A. Quarteroni. Fluid–structure algorithms based on Steklov–Poincaré operators. Comput. Methods Appl. Mech. Engrg., 195:5797–5812, 2008.
L. Halpern. Schwarz waveform relaxation algorithms. In Domain Decomposition Methods in Science and Engineering XVII, volume 60 of Lecture Notes in Computational Science and Engineering, pages 155–164. Springer, 2008.
R. Kornhuber. On constrained Newton linearization and multigrid for variational inequalities. Numer. Math., 91:699–721, 2002.
A. Quarteroni and A. Valli. Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications, 1999.
P. Sochala, A. Ern, and S. Piperno. Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows. Comput. Methods Appl. Mech. Engrg., 198:2122–2136, 2009.
N.J. Walkington. Convergence of the discontinuous Galerkin method for discontinuous solutions. SIAM J. Numer. Anal., 42:1801–1817, 2005.
B. Wiese and G. Nützmann. Transient leakance and infiltration characteristics during lake bank filtration. Ground Water, 47(1):57–68, 2009.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Berninger, H., Kornhuber, R., Sander, O. (2013). Heterogeneous Substructuring Methods for Coupled Surface and Subsurface Flow. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_50
Download citation
DOI: https://doi.org/10.1007/978-3-642-35275-1_50
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35274-4
Online ISBN: 978-3-642-35275-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)