A Dual–Mixed Finite Element Method for the Brinkman Problem

DOI10.5802/smai-jcm.7zbMath1416.76112OpenAlexW2562489441MaRDI QIDQ4967331

Noel J. Walkington, Jason S. Howell, Michael Neilan

Publication date: 3 July 2019

Published in: The SMAI journal of computational mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/smai-jcm.7

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (6)

A note on the uniform inf-sup condition for the Brinkman problem in highly heterogeneous media ⋮ A conforming discontinuous Galerkin finite element method for Brinkman equations ⋮ A uniform and pressure-robust enriched Galerkin method for the Brinkman equations ⋮ A Uniformly Robust H(DIV) Weak Galerkin Finite Element Methods for Brinkman Problems ⋮ An H1-conforming virtual element for Darcy and Brinkman equations ⋮ A new DG method for a pure-stress formulation of the Brinkman problem with strong symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inf-sup conditions for twofold saddle point problems
• Numerical computations with \(H(\mathop{div})\)-finite elements for the Brinkman problem
• Homogenization of a Darcy-Stokes system modeling vuggy porous media
• A family of higher order mixed finite element methods for plane elasticity
• A discrete de Rham complex with enhanced smoothness
• Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system
• A strongly conservative finite element method for the coupling of Stokes and Darcy flow
• Mixed finite elements in \(\mathbb{R}^3\)
• Analysis of finite element methods for the Brinkman problem
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes
• Computations with finite element methods for the Brinkman problem
• Analysis of a pseudostress-based mixed finite element method for the Brinkman model of porous media flow
• Mixed finite elements, compatibility conditions, and applications. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, June 26--July 1, 2006
• H(div)-CONFORMING FINITE ELEMENTS FOR THE BRINKMAN PROBLEM
• Convergence of a family of Galerkin discretizations for the Stokes-Darcy coupled problem
• Efficient rectangular mixed finite elements in two and three space variables
• Homogenization and Numerical Simulation of Flow in Geometries with Textile Microstructures
• A New Divergence-Free Interpolation Operator with Applications to the Darcy–Stokes–Brinkman Equations
• Mixed and Hybrid Finite Element Methods
• A family of nonconforming elements for the Brinkman problem
• A Robust Finite Element Method for Darcy--Stokes Flow
• Finite Element Methods for Maxwell's Equations
• A nonconforming rectangular finite element pair for the Darcy–Stokes–Brinkman model
• Strong coupling of finite element methods for the Stokes-Darcy problem
• ON A HIERARCHY OF APPROXIMATE MODELS FOR FLOWS OF INCOMPRESSIBLE FLUIDS THROUGH POROUS SOLIDS
• Dual-mixed finite element methods for the Navier-Stokes equations
• A Mixed Formulation for the Brinkman Problem

This page was built for publication: A Dual–Mixed Finite Element Method for the Brinkman Problem