A projective hybridizable discontinuous Galerkin mixed method for second-order diffusion problems

DOI10.1016/j.apm.2019.05.054zbMath1481.65223OpenAlexW2948523731MaRDI QIDQ1985142

Vincent Fontaine, Thierry Alex Mara, Loic Dijoux

Publication date: 7 April 2020

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://hal.univ-reunion.fr/hal-02289119/file/R3-HRTP.pdf

zbMATH Keywords

hybridizable discontinuous Galerkin\(h\) and \(p\) refinementshigher-order Raviart-Thomas spaceprojective-based stabilization functionsimplified postprocessing

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

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Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems ⋮ Families of hybridized interior penalty discontinuous Galerkin methods for locally degenerate advection-diffusion-reaction problems

Uses Software

• CSparse

Cites Work

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• An HDG method for convection diffusion equation
• To CG or to HDG: A comparative study
• An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations
• A hybridizable discontinuous Galerkin method for Stokes flow
• A hybridized discontinuous Galerkin method with reduced stabilization
• An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
• Discontinuous skeletal gradient discretisation methods on polytopal meshes
• A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field
• Hybrid high-order methods for variable-diffusion problems on general meshes
• Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media
• High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows
• A parallel and adaptive hybridized discontinuous Galerkin method for anisotropic nonhomogeneous diffusion
• Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods
• Conditions for superconvergence of HDG methods for second-order elliptic problems
• Static Condensation, Hybridization, and the Devising of the HDG Methods
• A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods
• A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
• Direct Methods for Sparse Linear Systems
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Mixed and Hybrid Finite Element Methods
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Hybrid Discontinuous Galerkin Methods with Relaxed H(div)-Conformity for Incompressible Flows. Part I
• Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
• A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems