Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Authors:
Douglas N. Arnold;Franco Brezzi;Bernardo Cockburn;L. Donatella Marini
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2001

Citing 0
Cited 227

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Thehp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations

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Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods

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A feasibility study for discontinuous Galerkin discretization with embedded Dirichlet boundary condition

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A Family of Discontinuous Galerkin Finite Elements for the Reissner--Mindlin Plate

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An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems

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Two-Level Non-Overlapping Schwarz Preconditioners for a Discontinuous Galerkin Approximation of the Biharmonic Equation

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Mixed Discontinuous Galerkin Approximation of the Maxwell Operator: Non-Stabilized Formulation

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Energy Norm shape A Posteriori Error Estimation for Mixed Discontinuous Galerkin Approximations of the Stokes Problem

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Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems

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Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems

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Discontinuous Galerkin Method for Linear Free-Surface Gravity Waves

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Mixed Discontinuous Galerkin Methods for Darcy Flow

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An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method

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Discontinuous Galerkin methods for coupled flow and reactive transport problems

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p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

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A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics

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A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate

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Mixed discontinuous Galerkin methods for Darcy flow

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An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems

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An a posteriori error estimate for the local discontinuous Galerkin method

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Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the Biharmonic equation

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Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation

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Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the stokes problem

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Block preconditioners for LDG discretizations of linear incompressible flow problems

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Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems

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Discontinuous Galerkin method for linear free-surface gravity waves

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Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations

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Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

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A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations

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Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes

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A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes

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Approximation of functionally graded plates with non-conforming finite elements

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BDDC methods for discontinuous Galerkin discretization of elliptic problems

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An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations

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The Computation of a Locally Conservative Stress for the Continuous Galerkin Method for Compressible Linearly Elastic Materials

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An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations

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A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D high frequency electromagnetic scattering in dispersive inhomogeneous media

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Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

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Analysis and application of the IIPG method to quasilinear nonstationary convection-diffusion problems

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LBB stability of a mixed Galerkin finite element pair for fluid flow simulations

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Discontinuous Galerkin Methods Based on Weighted Interior Penalties for Second Order PDEs with Non-smooth Coefficients

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Vanishing Moment Method and Moment Solutions for Fully Nonlinear Second Order Partial Differential Equations

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Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems

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On L2-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data

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Enrichment textures for detailed cutting of shells

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A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics

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Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations

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A Posteriori Error Control for a Weakly Over-Penalized Symmetric Interior Penalty Method

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An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

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The WKB Local Discontinuous Galerkin Method for the Simulation of Schrödinger Equation in a Resonant Tunneling Diode

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A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems

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A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

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Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation

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An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations

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Flexible simulation of deformable models using discontinuous Galerkin FEM

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Discontinuous Galerkin methods for coupled flow and reactive transport problems

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Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma

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Stability and error analysis of mixed finite-volume methods for advection dominated problems

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Discretisation of diffusive fluxes on hybrid grids

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An Intrinsically Parallel Finite Element Method

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The L2-Optimality of the IIPG Method for Odd Degrees of Polynomial Approximation in 1D

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A two-mesh adaptive mesh refinement technique for SN neutral-particle transport using a higher-order DGFEM

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A fully conservative Eulerian-Lagrangian method for a convection-diffusion problem in a solenoidal field

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Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection-diffusion equation

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An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

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A first-order system approach for diffusion equation. II: Unification of advection and diffusion

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Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations

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Abstract

We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.