Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator

DOI10.1016/j.camwa.2022.08.043OpenAlexW4294795188WikidataQ114201397 ScholiaQ114201397MaRDI QIDQ2094320

Zhuoran Wang, Jiangguo Liu, Ruishu Wang

Publication date: 28 October 2022

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.08.043

zbMATH Keywords

Stokes flowquadrilateral meshesweak Galerkinlifting operatorcuboidal hexahedralocal Arbogast-Correa/Tao spaces

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) 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 (2)

Penalty-free any-order weak Galerkin FEMs for linear elasticity on quadrilateral meshes ⋮ A locking-free weak Galerkin finite element method for linear elasticity problems

Cites Work

• Unnamed Item
• A weak Galerkin finite element scheme for solving the stationary Stokes equations
• Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow
• A hybridizable discontinuous Galerkin method for Stokes flow
• On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime
• A weak Galerkin finite element method for the Maxwell equations
• A stable finite element for the Stokes equations
• A weak Galerkin least-squares finite element method for div-curl systems
• Construction of \(H({\operatorname{div}})\)-conforming mixed finite elements on cuboidal hexahedra
• A systematic study on weak Galerkin finite element methods for second order elliptic problems
• A divergence-free velocity reconstruction for incompressible flows
• A uniformly stable Fortin operator for the Taylor-Hood element
• Development of pressure-robust discontinuous Galerkin finite element methods for the Stokes problem
• A staggered DG method of minimal dimension for the Stokes equations on general meshes
• Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes
• Coupling Arbogast-Correa and Bernardi-Raugel elements to resolve coupled Stokes-Darcy flow problems
• A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
• Penalty-free any-order weak Galerkin FEMs for elliptic problems on quadrilateral meshes
• The MINI mixed finite element for the Stokes problem: an experimental investigation
• A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements
• A pressure-robust virtual element method for the Stokes problem
• A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes
• Convergence analysis of triangular MAC schemes for two dimensional Stokes equations
• A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
• Modular grad-div stabilization for the incompressible non-isothermal fluid flows
• Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension
• Stokes Complexes and the Construction of Stable Finite Elements with Pointwise Mass Conservation
• Conforming and divergence-free Stokes elements on general triangular meshes
• Divergence-free finite elements on tetrahedral grids for $k\ge6$
• A weak Galerkin mixed finite element method for second order elliptic problems
• Optimal and Pressure-Independent L² Velocity Error Estimates for a Modified Crouzeix-Raviart Stokes Element with BDM Reconstructions
• Stability of Higher-Order Hood–Taylor Methods
• Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
• Approximation by quadrilateral finite elements
• The Scott-Vogelius finite elements revisited
• A Weak Galerkin Finite Element Method for the Linear Elasticity Problem in Mixed Form
• A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes
• A weak Galerkin finite element scheme for the Cahn-Hilliard equation
• A note on the devising of superconvergent HDG methods for Stokes flow byM-decompositions
• Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes
• Mixed Finite Element Methods and Applications
• Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
• Pressure Robust Weak Galerkin Finite Element Methods for Stokes Problems
• A Pressure-Robust Embedded Discontinuous Galerkin Method for the Stokes Problem by Reconstruction Operators
• The Hitchhiker's Guide to the Virtual Element Method
• Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations with Continuous Pressure Finite Elements
• On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

This page was built for publication: Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator