Construction of \(H({\operatorname{div}})\)-conforming mixed finite elements on cuboidal hexahedra

DOI10.1007/S00211-018-0998-7zbMath1414.65031arXiv1807.01416OpenAlexW3101511289MaRDI QIDQ1740499

Zhen Tao, Todd Arbogast

Publication date: 30 April 2019

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.01416

zbMATH Keywords

mixed finite elements

Mathematics Subject Classification ID

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) Approximation by polynomials (41A10)

Related Items (10)

Direct serendipity and mixed finite elements on convex quadrilaterals ⋮ Penalty-free any-order weak Galerkin FEMs for elliptic problems on quadrilateral meshes ⋮ A div FOSLS method suitable for quadrilateral RT and hexahedral RTN \(H(\operatorname{div})\)-elements ⋮ A stabilized finite element method on nonaffine grids for time-harmonic Maxwell's equations ⋮ Penalty-free any-order weak Galerkin FEMs for linear elasticity on quadrilateral meshes ⋮ A direct mixed-enriched Galerkin method on quadrilaterals for two-phase Darcy flow ⋮ Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes ⋮ Coupling Arbogast-Correa and Bernardi-Raugel elements to resolve coupled Stokes-Darcy flow problems ⋮ Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator ⋮ A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Cites Work

• Unnamed Item
• Mixed finite element methods for general quadrilateral grids
• Two families of mixed finite elements for second order elliptic problems
• Mixed finite elements for second order elliptic problems in three variables
• Finite element differential forms on curvilinear cubic meshes and their approximation properties
• Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension
• HexahedralH(div) andH(curl) finite elements
• Superconvergence byM-decompositions. Part III: Construction of three-dimensional finite elements
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Finite Element Methods for Navier-Stokes Equations
• Mixed and Hybrid Finite Element Methods
• Nonconforming elements in least-squares mixed finite element methods
• Approximation of H(div) with High-Order Optimal Finite Elements for Pyramids, Prisms and Hexahedra
• Finite element differential forms on cubical meshes
• QuadrilateralH(div) Finite Elements

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