A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems

DOI10.1137/20M1316962zbMath1456.65101arXiv1810.03095MaRDI QIDQ5147974

Mohammad Alhawwary, Zhi Jian Wang

Publication date: 29 January 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.03095

zbMATH Keywords

interior penaltylocal discontinuous GalerkinBassi and Rebaycompact discontinuous Galerkincombined-mode Fourier analysislinear diffusion analysis

Mathematics Subject Classification ID

Diffusion (76R50) Heat equation (35K05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Turbulence (76F99) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (5)

Data-driven eigensolution analysis based on a spatio-temporal Koopman decomposition, with applications to high-order methods ⋮ Fully-discrete spatial eigenanalysis of discontinuous spectral element methods: insights into well-resolved and under-resolved vortical flows ⋮ Discontinuous Galerkin spectral element method for shock capturing with summation by parts properties ⋮ Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property ⋮ The spectral difference Raviart-Thomas method for two and three-dimensional elements and its connection with the flux reconstruction formulation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A study of viscous flux formulations for a \(p\)-multigrid spectral volume Navier Stokes solver
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
• An analysis of the discontinuous Galerkin method for wave propagation problems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Correction to: ``The BR1 scheme is stable for the compressible Navier-Stokes equations
• High-order methods for computational fluid dynamics: a brief review of compact differential formulations on unstructured grids
• A priori and a posteriori evaluations of sub-grid scale models for the Burgers' equation
• An explicit expression for the penalty parameter of the interior penalty method
• Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
• Fourier type error analysis of the direct discontinuous Galerkin method and its variations for diffusion equations
• Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods
• Non-modal analysis of spectral element methods: towards accurate and robust large-eddy simulations
• Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: eigen-structure analysis based on Fourier approach
• On the behaviour of fully-discrete flux reconstruction schemes
• Fourier analysis and evaluation of DG, FD and compact difference methods for conservation laws
• High-order flux reconstruction schemes with minimal dispersion and dissipation
• Estimation of penalty parameters for symmetric interior penalty Galerkin methods
• Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/\(hp\) methods
• High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
• Energy stable flux reconstruction schemes for advection-diffusion problems
• AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS
• A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss–Lobatto Discontinuous Galerkin Spectral Element Methods
• Sharp cutoff versus smooth filtering in large eddy simulation
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations
• Stability of Energy Stable Flux Reconstruction for the Diffusion Problem Using Compact Numerical Fluxes
• Performance of Discontinuous Galerkin Methods for Elliptic PDEs
• Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence
• The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems

This page was built for publication: A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems