Fourier type error analysis of the direct discontinuous Galerkin method and its variations for diffusion equations

DOI10.1007/s10915-011-9564-5zbMath1255.65165OpenAlexW2007617472MaRDI QIDQ1930415

Mengping Zhang, Jue Yan

Publication date: 11 January 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9564-5

zbMATH Keywords

stabilityconvergenceconsistencydiffusion equationdiscontinuous Galerkin methodsupraconvergence

Mathematics Subject Classification ID

Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (12)

Superconvergence study of the direct discontinuous Galerkin method and its variations for diffusion equations ⋮ The direct discontinuous Galerkin methods with implicit-explicit Runge-Kutta time marching for linear convection-diffusion problems ⋮ Analysis and development of adjoint-based h-adaptive direct discontinuous Galerkin method for the compressible Navier-Stokes equations ⋮ A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier-Stokes equations ⋮ Fourier type super convergence study on DDGIC and symmetric DDG methods ⋮ On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations ⋮ A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems ⋮ An Efficient DDG/FV Hybrid Method for 3D Viscous Flow Simulations on Tetrahedral Grids ⋮ A new approach for admissibility analysis of the direct discontinuous Galerkin method through Hilbert matrices ⋮ Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order ⋮ Fourier analysis of local discontinuous Galerkin methods for linear parabolic equations on overlapping meshes ⋮ Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations

Cites Work

• Unnamed Item
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Compatible algorithms for coupled flow and transport
• A weakly over-penalized symmetric interior penalty method
• A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes
• Superconvergence and time evolution of discontinuous Galerkin finite element solutions
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• A discontinuous \(hp\) finite element method for diffusion problems
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods
• Central local discontinuous galerkin methods on overlapping cells for diffusion equations
• AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS
• L²stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A New Direct Discontinuous Galerkin Method with Symmetric Structure for Nonlinear Diffusion Equations
• The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections
• The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives

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