A Robust Finite Element Method for Darcy--Stokes Flow

From MaRDI portal
Publication:4785831

DOI10.1137/S0036142901383910zbMath1037.65120MaRDI QIDQ4785831

Ragnar Winther, Kent-André Mardal, Xue-Cheng Tai

Publication date: 5 January 2003

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)




Related Items (only showing first 100 items - show all)

Robust nonconforming polynomial finite elements over quadrilateralsA uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problemPreconditioning discretizations of systems of partial differential equationsStable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral gridsA domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integralsA conservative stable finite element method for Stokes flow and nearly incompressible linear elasticity on rectangular gridA note on the uniform inf-sup condition for the Brinkman problem in highly heterogeneous mediaStability of Lagrange elements for the mixed LaplacianEdge stabilization for the generalized Stokes problem: a continuous interior penalty methodA posteriori error estimation based on conservative flux reconstruction for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem on anisotropic meshesNodal finite element de Rham complexesRobust three-field finite element methods for Biot's consolidation model in poroelasticitySpectral methods based on new formulations for coupled Stokes and Darcy equationsAnalysis of a mixed DG method for stress-velocity formulation of the Stokes equationsA coupling of weak Galerkin and mixed finite element methods for poroelasticityUniformly convergent cubic nonconforming element for Darcy-Stokes problemA Sommerfeld non-reflecting boundary condition for the wave equation in mixed formA global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flowsA discrete de Rham complex with enhanced smoothnessMulti-level Monte Carlo weak Galerkin method with nested meshes for stochastic Brinkman problemA new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limitsTwo robust nonconforming \(H^2\)-elements for linear strain gradient elasticityNonstandard finite element de Rham complexes on cubical meshesLow-rank solvers for unsteady Stokes-Brinkman optimal control problem with random dataHigh accuracy analysis of a nonconforming rectangular finite element method for the Brinkman modelA lowest-degree conservative finite element scheme for incompressible Stokes problems on general triangulationsRobustness of a spline element method with constraintsA DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfacesA divergence free weak virtual element method for the Stokes problem on polytopal meshesParameter-Robust Discretization and Preconditioning of Biot's Consolidation ModelA Least-Squares Formulation for the Shallow Water Equations with Small ViscosityGlobal well-posedness of an initial-boundary value problem of the 2-D incompressible Navier-Stokes-Darcy systemContinuous mixed finite elements for the second order elliptic equation with a low order termAn H1-conforming virtual element for Darcy and Brinkman equationsComputationally efficient modular nonlinear filter stabilization for high Reynolds number flowsLong time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblemsComputations with finite element methods for the Brinkman problemRobin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface conditionA unified stabilized method for Stokes' and Darcy's equationsA NEW MINIMIZATION PRINCIPLE FOR THE POISSON EQUATION LEADING TO A FLEXIBLE FINITE ELEMENT APPROACHDiscontinuous Galerkin and mimetic finite difference methods for coupled Stokes-Darcy flows on polygonal and polyhedral gridsMixed finite element methods for the Poisson equation using biorthogonal and quasi-biorthogonal systemsEqual-order finite elements with local projection stabilization for the Darcy-brinkman equationsAnalysis of finite element methods for the Brinkman problemNon-iterative domain decomposition methods for a non-stationary Stokes-Darcy model with Beavers-Joseph interface conditionA unified stabilized mixed finite element method for coupling Stokes and Darcy flowsA unified mixed formulation naturally coupling Stokes and Darcy flowsStabilized finite elements for transient flow problems on varying spatial meshesMortar multiscale finite element methods for Stokes-Darcy flowsA parallel domain decomposition method for coupling of surface and groundwater flowsGrad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equationsStabilized continuous and discontinuous Galerkin techniques for Darcy flowA globally divergence-free weak Galerkin method for Brinkman equationsUniformly convergent \(H(\mathrm{div})\)-conforming rectangular elements for Darcy-Stokes problemQuasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-problemA posteriori error estimate for the Stokes-Darcy systemApplication of a minimal compatible element to incompressible and nearly incompressible continuum mechanicsA pressure-robust virtual element method for the Stokes problemA hybrid high-order discretisation of the Brinkman problem robust in the Darcy and Stokes limitsA nonconforming rectangular finite element pair for the Darcy–Stokes–Brinkman modelTopology optimization of Stokes flow with traction boundary conditions using low-order finite elementsUnnamed ItemOn the use of divergence balanced \(\mathbf{H}(\operatorname{div})\)-\(L^2\) pair of approximation spaces for divergence-free and robust simulations of Stokes, coupled Stokes-Darcy and Brinkman problemsOn a MIC(0) preconditioning of non-conforming mixed FEM elliptic problemsISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE DARCY–STOKES–BRINKMAN EQUATIONSNumerical computations with \(H(\mathop{div})\)-finite elements for the Brinkman problemA new finite element method for Darcy-Stokes-Brinkman equationsSuperconvergence analysis of FEMs for the Stokes-Darcy system\(H\)(div) conforming finite element methods for the coupled Stokes and Darcy problemAnalysis of a discontinuous finite element method for the coupled Stokes and Darcy problemsThe nonconforming virtual element method for the Darcy-Stokes problemA mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulationFast numerical schemes related to curvature minimization: a brief and elementary reviewRobust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal formOn classical iterative subdomain methods for the Stokes-Darcy problemHybridized weak Galerkin finite element methods for Brinkman equationsA stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methodsUnified finite element discretizations of coupled Darcy-Stokes flowAn unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluidBoundary integral solutions of coupled Stokes and Darcy flowsDomain decomposition for coupled Stokes and Darcy flowsLow-order nonconforming brick elements for the 3D Brinkman modelNumerical computation of Brinkman flow with stable mixed element methodA Dual–Mixed Finite Element Method for the Brinkman ProblemA general approach to transforming finite elementsAnalysis of the stabilized element free Galerkin approximations to the Stokes equationsA computational study of stabilized, low-order \(C^{0}\) finite element approximations of Darcy equationsFractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEMWeakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flowTwo robust virtual element methods for the Brinkman equationsGeneralized local projection stabilized nonconforming finite element methods for Darcy equationsA Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equationStokes-Darcy boundary integral solutions using preconditionersThe Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flowsRobust BDDC algorithms for the Brinkman problem with HDG discretizationsMultigrid analysis for the time dependent Stokes problemAn absolutely stable weak Galerkin finite element method for the Darcy-Stokes problemNonconforming polynomial mixed finite element for the Brinkman problem over quadrilateral meshesA low-degree strictly conservative finite element method for incompressible flows on general triangulationsConforming and divergence-free Stokes elements on general triangular meshes




This page was built for publication: A Robust Finite Element Method for Darcy--Stokes Flow