Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

By Marco Discacciati, Alfio Maria Quarteroni. 2004

161 citations recorded by the source corpus.

We consider a Galerkin Finite Element approximation of the Stokes–Darcy problem which models the coupling between surface and groundwater flows. Then we propose an iterative subdomain method for its solution, inspired to the domain decomposition theory. The convergence analysis that we develop is based on the properties of the discrete Steklov–Poincaré operators associated to the given coupled problem. An optimal preconditioner for Krylov methods is proposed and analyzed.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e28e252fcb4cfb28f5bb6afbb71310987594f4e1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Neurobiology of Aging: Contents (2005, unknown): “Complex coefficient matrices, however, do arise in some cases; see, e.g., Bobrovnikova and Vavasis (2000), Mahawar and Sarin (2003) and Strang (1986, page 117).”
A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow (2007, unknown): “Keywords Porous media flow, Stokes equations, Darcy’s law, Multi-modeling prob- lems, Two-grid method.”
Computational issues related to iterative coupling of subsurface and channel flows (2007, methodology): “In our setting,UΓ contains three velocity components at each interface node, whereas in [5,6] UΓ is composed of only the normal component.”
Coupling Darcy and Stokes equations for porous media with cracks (2005, methodology): “In [12,13], a domain decomposition is introduced, with one subdomain for the medium and another one for the fluid, and an iterative procedure for solving the resulting system is analyzed (see also [9], Sect.”
A decoupling two‐grid algorithm for the mixed Stokes‐Darcy model with the Beavers‐Joseph interface condition (2014, unknown): “Let H be a positive parameter tending to 0, τH be a quasi-uniform triangulation of the domain into triangles or quadrilaterals with diameters bounded by H , as well as compatible and quasiuniform on as described in [17] and [30].”
Asymptotic analysis of the differences between the Stokes–Darcy system with different interface conditions and the Stokes–Brinkman system☆ (2010, background): “…the components of the coupled Navier-Stokes-Darcy or StokesDarcy systems, two interface conditions are well-accepted: the continuity of the normal velocity across the interface which is a consequence of the conservation of mass, and the balance of the stress force normal to the interface.”
A parallel domain decomposition method for coupling of surface and groundwater flows (2009, background): “fh ¼f v 2 Hfh : v � njC ¼ 0g. The above discrete operators T ph and T fh have the following properties. Lemma 14 (Lemma 1, Section 4.1 of [ 5 ]).”