A unified stabilized method for Stokes' and Darcy's equations

From MaRDI portal

Publication:2433781

Jump to:navigation, search

DOI10.1016/j.cam.2005.11.022zbMath1101.76032OpenAlexW2041589227MaRDI QIDQ2433781

Erik Burman, Peter Hansbo

Publication date: 30 October 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.11.022

zbMATH Keywords

finite element method inf-sup condition Nitsche's method

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

MINIMAL LOCALLY STABILIZED Q1-Q0 SCHEMES FOR THE GENERALIZED STOKES PROBLEM ⋮ A uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem ⋮ A Newton type linearization based two grid method for coupling fluid flow with porous media flow ⋮ A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals ⋮ Finite element method for the Stokes-Darcy problem with a new boundary condition ⋮ A stabilized mixed formulation for unsteady Brinkman equation based on the method of horizontal lines ⋮ A priori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations ⋮ A strongly conservative hybrid DG/mixed FEM for the coupling of Stokes and Darcy flow ⋮ Combining a level-set method and a mixed stabilized P1/P1 formulation for coupling Stokes-Darcy flows ⋮ A numerical study of fluids with pressure-dependent viscosity flowing through a rigid porous medium ⋮ Stabilized Crouzeix-Raviart element for Darcy-Forchheimer model ⋮ The two-level stabilized finite element method based on multiscale enrichment for the Stokes eigenvalue problem ⋮ Weak imposition of the slip boundary condition on curved boundaries for Stokes flow ⋮ Spectral methods based on new formulations for coupled Stokes and Darcy equations ⋮ A numerical method for a model of two-phase flow in a coupled free flow and porous media system ⋮ A mixed and nonconforming FEM with nonmatching meshes for a coupled Stokes-Darcy model ⋮ A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows ⋮ A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity ⋮ A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits ⋮ Stabilized Lowest-Order Finite Element Approximation for Linear Three-Field Poroelasticity ⋮ Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form ⋮ The numerical methods for the coupled fluid flow under the leak interface condition of the friction-type ⋮ First-order system least-squares finite element method for singularly perturbed Darcy equations ⋮ Primal discontinuous Galerkin methods for time-dependent coupled surface and subsurface flow ⋮ A DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfaces ⋮ An extended finite element method for coupled Darcy–Stokes problems ⋮ Numerical analysis of the coupling of free fluid with a poroelastic material ⋮ A polytopal method for the Brinkman problem robust in all regimes ⋮ Numerical approximation with Nitsche's coupling of transient Stokes/Darcy's flow problems applied to hemodynamics ⋮ Mortar finite element discretization of a model coupling Darcy and Stokes equations ⋮ A Uniformly Robust H(DIV) Weak Galerkin Finite Element Methods for Brinkman Problems ⋮ Analysis of a diffuse interface method for the Stokes-Darcy coupled problem ⋮ Some multilevel decoupled algorithms for a mixed Navier-Stokes/Darcy model ⋮ Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems ⋮ Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition ⋮ A stabilized finite element method for finite-strain three-field poroelasticity ⋮ Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit ⋮ Coupling nonlinear Stokes and Darcy flow using mortar finite elements ⋮ Equal-order finite elements with local projection stabilization for the Darcy-brinkman equations ⋮ Stabilized finite element method for the stationary mixed Stokes-Darcy problem ⋮ Non-iterative domain decomposition methods for a non-stationary Stokes-Darcy model with Beavers-Joseph interface condition ⋮ P1/P0+ elements for incompressible flows with discontinuous material properties ⋮ A unified stabilized mixed finite element method for coupling Stokes and Darcy flows ⋮ A unified mixed formulation naturally coupling Stokes and Darcy flows ⋮ A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes-Darcy coupled problem ⋮ Analysis of a stabilized finite element method for fluid flows through a porous interface ⋮ Convergence analysis of a new multiscale finite element method with the \(P_1/P_0\) element for the incompressible flow ⋮ Approximation of coupled Stokes-Darcy flow in an axisymmetric domain ⋮ Mortar multiscale finite element methods for Stokes-Darcy flows ⋮ Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility ⋮ Some low order nonconforming mixed finite elements combined with Raviart-Thomas elements for a coupled Stokes-Darcy model ⋮ Analysis of a pseudostress-based mixed finite element method for the Brinkman model of porous media flow ⋮ On the solution of the coupled Navier-Stokes and Darcy equations ⋮ Extension of NXFEM to nonconforming finite elements ⋮ Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem ⋮ Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems ⋮ Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman model of porous media flow ⋮ Stabilized explicit coupling for fluid-structure interaction using Nitsche's method ⋮ Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics ⋮ An overlapping local projection stabilization for Galerkin approximations of Stokes and Darcy flow problems ⋮ A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model ⋮ A stabilized hybrid mixed DGFEM naturally coupling Stokes-Darcy flows ⋮ Multimesh finite element methods: solving PDEs on multiple intersecting meshes ⋮ A hybrid high-order discretisation of the Brinkman problem robust in the Darcy and Stokes limits ⋮ A nonconforming rectangular finite element pair for the Darcy–Stokes–Brinkman model ⋮ Topology optimization of Stokes flow with traction boundary conditions using low-order finite elements ⋮ An adaptive stabilized finite element method for the Darcy's equations with pressure dependent viscosities ⋮ A posteriori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations ⋮ Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems ⋮ Numerical computations with \(H(\mathop{div})\)-finite elements for the Brinkman problem ⋮ Nitsche's type stabilized finite element method for the fully mixed Stokes-Darcy problem with Beavers-Joseph conditions ⋮ \(H\)(div) conforming finite element methods for the coupled Stokes and Darcy problem ⋮ Coupling Arbogast-Correa and Bernardi-Raugel elements to resolve coupled Stokes-Darcy flow problems ⋮ A macroelement stabilization for mixed finite element/finite volume discretizations of multiphase poromechanics ⋮ Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form ⋮ On classical iterative subdomain methods for the Stokes-Darcy problem ⋮ An analysis on the penalty and Nitsche's methods for the Stokes-Darcy system with a curved interface ⋮ Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual-porosity-Navier-Stokes model ⋮ A strongly conservative finite element method for the coupling of Stokes and Darcy flow ⋮ Analysis of time-dependent Navier–Stokes flow coupled with Darcy flow ⋮ Boundary integral solutions of coupled Stokes and Darcy flows ⋮ A two-level enriched finite element method for a mixed problem ⋮ Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow ⋮ A diffuse interface method for the Navier-Stokes/Darcy equations: perfusion profile for a patient-specific human liver based on MRI scans ⋮ Analysis of fully-mixed finite element methods for the Stokes-Darcy coupled problem ⋮ Generalized local projection stabilized nonconforming finite element methods for Darcy equations ⋮ Existence of a weak solution for the fully coupled Navier-Stokes/Darcy-transport problem ⋮ A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation ⋮ Stokes-Darcy boundary integral solutions using preconditioners ⋮ A discretization and multigrid solver for a Darcy-Stokes system of three dimensional vuggy porous media

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:2433781&oldid=15095351"