Optimal maximum-norm estimate of the LDG method for singularly perturbed convection-diffusion problem

DOI10.1016/j.aml.2022.107947zbMath1492.65214OpenAlexW4205670463WikidataQ110648599 ScholiaQ110648599MaRDI QIDQ2077101

Yao Cheng, Yanhua Liu, Li Yan, Xue-Song Wang

Publication date: 22 February 2022

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2022.107947

zbMATH Keywords

convection-diffusionsingularly perturbedlocal discontinuous Galerkin methodnumerical fluxmaximum-norm estimate

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (8)

Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem ⋮ Local discontinuous Galerkin method for a singularly perturbed fourth-order problem of reaction-diffusion type ⋮ Local discontinuous Galerkin method on graded meshes for a third‐order singularly perturbed problem ⋮ Optimal pointwise convergence of the LDG method for singularly perturbed convection-diffusion problem ⋮ The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers ⋮ Local discontinuous Galerkin method for a third-order singularly perturbed problem of convection-diffusion type ⋮ Analysis of an LDG-FEM for a two-dimensional singularly perturbed convection-reaction-diffusion problem with interior and boundary layers ⋮ Local discontinuous Galerkin method for a third‐order singularly perturbed problem of reaction–diffusion type

Cites Work

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• \(L^\infty\) estimation of the LDG method for 1-D singularly perturbed convection-diffusion problems
• Pointwise error estimates for a streamline diffusion finite element scheme
• Layer-adapted meshes for convection-diffusion problems
• Local analysis of the local discontinuous Galerkin method with generalized alternating numerical flux for one-dimensional singularly perturbed problem
• Supercloseness of linear finite element method on Bakhvalov-type meshes for singularly perturbed convection-diffusion equation in 1D
• On the local discontinuous Galerkin method for singularly perturbed problem with two parameters
• On discontinuous Galerkin finite element method for singularly perturbed delay differential equations
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem
• Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations
• Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer
• Application of generalized Gauss–Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• The Mathematical Theory of Finite Element Methods
• Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems

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