zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A parallel domain decomposition method for coupling of surface and groundwater flows. (English) Zbl 1229.76048
Summary: In this paper, we construct a robust parallel method based on a recently developed non-overlapping domain decomposition methodology to accurately model natural coupling of surface and groundwater flows. Stokes and Darcy equations are formulated and solved within the surface and subsurface regions, respectively. A new type of Robin-Robin boundary condition is proposed on the common boundary for the coupling of those systems. The formulation provides great flexibility for multi-physics coupling and is suitable for efficient parallel implementation. Meanwhile, it is stable with inherent system parameter variation. A numerical example is provided to verify the theory.
MSC:
76M10Finite element methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76D07Stokes and related (Oseen, etc.) flows
65Y05Parallel computation (numerical methods)
86A05Hydrology, hydrography, oceanography
References:
[1]Brezzi, F.; Fortin, M.: Mixed and hybrid finite element methods, (1991) · Zbl 0788.73002
[2]Ciarlet, P. G.: The finite element method for elliptic problems, (1979)
[3]Discacciati, M.; Miglio, E.; Quarteroni, A.: Mathematical and numerical models for coupling surface and groundwater flows, Appl. num. Math. 43, 57-74 (2002) · Zbl 1023.76048 · doi:10.1016/S0168-9274(02)00125-3
[4]Discacciati, M.; Quarteroni, A.: Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations, Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, 3-20 (2003)
[5]Discacciati, M.; Quarteroni, A.: Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations, Comput. visual. Sci. 6, 93-103 (2004)
[6]Discacciati, M.; Quarteroni, A.; Valli, A.: Robin – Robin domain decomposition methods for the Stokes – Darcy coupling, SIAM J. Numer. anal. 45, 1246-1268 (2007) · Zbl 1139.76030 · doi:10.1137/06065091X
[7]Galvis, J. C.; Sarkis, M.: Balancing domain decomposition methods for mortar coupling Stokes – Darcy systems, (2006)
[8]Gartling, D.; Hickox, C.; Givler, R.: Simulation of coupled viscous and porous flow problems, Compos. fluid dyn. 7, 23-48 (1996) · Zbl 0879.76104 · doi:10.1080/10618569608940751
[9]Grisvard, P.: Elliptic problems in nonsmooth domains, (1985) · Zbl 0695.35060
[10]Jager, W.; Mikelic, A.: On the interface boundary condition of Beavers, Joseph and Saffman, SIAM J. Appl. math. 60, 1111-1127 (2000) · Zbl 0969.76088 · doi:10.1137/S003613999833678X
[11]Jiang, B.; Jr., J. C. Bruch; Sloss, J. M.: A nonoverlapping domain decomposition method for variational inequalities derived from free boundary problems, Numer. methods part. Diff. eqn. 22, 1-17 (2006) · Zbl 1114.65072 · doi:10.1002/num.20083
[12]Jiang, B.: Convergence analysis of P1 finite element method for free boundary problems on nonoverlapping subdomains, Comput. methods appl. Mech. engrg. 196, 371-378 (2006) · Zbl 1120.76325 · doi:10.1016/j.cma.2006.04.006
[13]Layton, W. L.; Schieweck, F.; Yotov, I.: Coupling fluid flow with porous media flow, SIAM J. Numer. anal. 40, 2195-2218 (2003) · Zbl 1037.76014 · doi:10.1137/S0036142901392766
[14]Lions, J. L.; Magenes, E.: Non-homogeneous boundary value problems and applications, Non-homogeneous boundary value problems and applications (1972)
[15]Mardal, K. A.; Tai, X. C.; Winther, R.: A robust finite element method for Darcy – Stokes flow, SIAM J. Numer. anal. 40, 1605-1631 (2002) · Zbl 1037.65120 · doi:10.1137/S0036142901383910
[16]Quarteroni, A.; Valli, A.: Domain decomposition method for partial differential equations, (1999)
[17]Riviere, B.; Yotov, I.: Locally conservative coupling of Stokes and Darcy flows, SIAM J. Numer. anal. 42, 1959-1977 (2005) · Zbl 1084.35063 · doi:10.1137/S0036142903427640
[18]Salinger, A.; Aris, R.; Derby, I.: Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains, Int. J. Numer. methods fluids 18, 1185-1209 (1994) · Zbl 0807.76039 · doi:10.1002/fld.1650181205