The weak Galerkin method for solving the incompressible Brinkman flow

DOI10.1016/j.cam.2016.04.031zbMath1338.76069OpenAlexW2346808155MaRDI QIDQ298189

Xiuli Wang, Ran Zhang, Qi Long Zhai

Publication date: 20 June 2016

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.2016.04.031

zbMATH Keywords

weak Galerkin finite element methodsdiscrete weak divergencediscrete weak gradientincompressible Brinkman

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

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Cites Work

• Unnamed Item
• Unnamed Item
• A \(C^0\)-weak Galerkin finite element method for the biharmonic equation
• A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
• An optimal-order \(L^2\)-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions
• A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods
• A weak Galerkin finite element method for the Maxwell equations
• A hybridized weak Galerkin finite element scheme for the Stokes equations
• Discontinuous Galerkin methods for coupled flow and reactive transport problems
• A weak Galerkin finite element method for second-order elliptic problems
• A computational study of the weak Galerkin method for second-order elliptic equations
• A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations
• Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
• Weak Galerkin finite element methods for Parabolic equations
• A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
• A quadratic finite volume element method for parabolic problems on quadrilateral meshes
• On the Stability of the Discontinuous Galerkin Method for the Heat Equation
• A weak Galerkin mixed finite element method for second order elliptic problems
• An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow
• Weak Galerkin Finite Element Methods on Polytopal Meshes
• Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
• On the Approximation of Miscible Displacement in Porous Media by a Method of Characteristics Combined with a Mixed Method
• Galerkin Methods for Miscible Displacement Problems in Porous Media
• Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method
• Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
• Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
• A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
• The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows
• A New Weak Galerkin Finite Element Scheme for the Brinkman Model
• Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
• Galerkin Finite Element Methods for Parabolic Problems
• A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations
• A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
• A weak Galerkin finite element method for the Stokes equations

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