Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations
type: Item
instance of: scholarly article
title: Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations
zbMATH Open document ID: 1465.65100
published in: Numerische Mathematik
publication date: 2021-04-28T00:00:00Z
review text: The author analyzes the multi-dimensional convection-diffusion equation with various boundary conditions using the direct discontinuous Galerkin (DDG) method. First, he presents the admissible parameter set for the DDG diffusive flux to ensure that the projection defined by the same DDG method to the elliptic problem is well-defined. Then he obtains the optimal projection error in \(L^2\). Finally, he presents \(L^2\) error estimates for the numerical solution to the nonlinear convection-diffusion with various boundary conditions.
reviewed by: J. Manimaran
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76R50
zbMATH DE Number: 7341057
zbMATH Keywords: convection-diffusion equations
zbMATH Keywords: discontinuous Galerkin methods
author: Hailiang Liu
MaRDI profile type: Publication
full work available at URL: s00211-021-01183-x
OpenAlex ID: W3134875676
cites work: An Interior Penalty Finite Element Method with Discontinuous Elements
cites work: Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
cites work: Finite Element Methods for Elliptic Equations Using Nonconforming Elements
cites work: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
cites work: A discontinuous \(hp\) finite element method for convection-diffusion problems
cites work: Q4952262
cites work: Performance of Discontinuous Galerkin Methods for Elliptic PDEs
cites work: Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
cites work: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
cites work: Optimal a priori error estimates for the \(hp\)-version of the local discontinuous Galerkin method for convection-diffusion problems
cites work: Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes
cites work: Q4162607
cites work: Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems
cites work: The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
cites work: A locally conservative LDG method for the incompressible Navier-Stokes equations
cites work: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
cites work: A hybrid reconstructed discontinuous Galerkin method for compressible flows on arbitrary grids
cites work: Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations
cites work: Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
cites work: TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
cites work: The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
cites work: A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
cites work: The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
cites work: A direct discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids
cites work: A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes
cites work: Recovery of normal derivatives from the piecewise \(L^2\) projection
cites work: Q5756148
cites work: An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
cites work: Mass preserving discontinuous Galerkin methods for Schrödinger equations
cites work: Q4109239
cites work: Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
cites work: An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations
cites work: A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems
cites work: Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations
cites work: The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
cites work: The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections
cites work: Maximum-Principle-Satisfying Third Order Discontinuous Galerkin Schemes for Fokker--Planck Equations
cites work: The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations
cites work: A discontinuous \(hp\) finite element method for diffusion problems
cites work: Riemann Solvers, the Entropy Condition, and Difference
cites work: A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
cites work: The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
cites work: An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
cites work: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
cites work: Q4952255
cites work: An Elliptic Collocation-Finite Element Method with Interior Penalties
cites work: Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems
cites work: Error Estimate on a Fully Discrete Local Discontinuous Galerkin Method for Linear Convection-Diffusion Problem
cites work: Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
cites work: An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
cites work: Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity
cites work: A direct discontinuous Galerkin method for the incompressible Navier-Stokes equations on arbitrary grids
cites work: Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
cites work: Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws
DOI: 10.1007/S00211-021-01183-X
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