zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
FETI and BDD preconditioners for Stokes-Mortar-Darcy systems. (English) Zbl 1189.35226
Summary: We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region, Darcy equations in the porous region, plus a coupling through an interface with Beaver-Joseph-Saffman transmission conditions. The discretization consists of P2/P1 triangular Taylor-Hood finite elements in the fluid region, the lowest order triangular Raviart-Thomas finite elements in the porous region, and the mortar piecewise constant Lagrange multipliers on the interface. We allow for nonmatching meshes across the interface. Due to the small values of the permeability parameter κ of the porous medium, the resulting discrete symmetric saddle point system is very ill conditioned. We design and analyze preconditioners based on the finite element by tearing and interconnecting (FETI) and balancing domain decomposition (BDD) methods and derive a condition number estimate of order C 1 (1+(1/κ)) for the preconditioned operator. In case the fluid discretization is finer than the porous side discretization, we derive a better estimate of order C 2 ((κ+1)/(κ+(h p ) 2 )) for the FETI preconditioner. Here h p is the mesh size of the porous side triangulation. The constants C 1 and C 2 are independent of the permeability κ, the fluid viscosity ν, and the mesh ratio across the interface. Numerical experiments confirm the sharpness of the theoretical estimates.
35Q30Stokes and Navier-Stokes equations
65N22Solution of discretized equations (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
76D07Stokes and related (Oseen, etc.) flows