Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems

DOI10.1007/S11075-022-01316-9OpenAlexW4280561001WikidataQ112879571 ScholiaQ112879571MaRDI QIDQ2098798

Yanjie Mei, Yao Cheng, Li Yan

Publication date: 22 November 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-022-01316-9

zbMATH Keywords

layer-adapted meshessingularly perturbedlocal discontinuous Galerkin methodbalanced-norm estimate

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (3)

Local discontinuous Galerkin method for a singularly perturbed fourth-order problem of reaction-diffusion type ⋮ An improved pointwise error estimate of the LDG method for 1-d singularly perturbed reaction-diffusion problem ⋮ A novel parameter-uniform numerical method for a singularly perturbed Volterra integro-differential equation

Cites Work

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• Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations
• Convergence analysis of the LDG method for singularly perturbed two-point boundary value problems
• Layer-adapted meshes for convection-diffusion problems
• On the local discontinuous Galerkin method for singularly perturbed problem with two parameters
• A weighted and balanced FEM for singularly perturbed reaction-diffusion problems
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer
• Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Uniform superconvergence analysis of the discontinuous Galerkin method for a singularly perturbed problem in 1-D
• A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• A parameter robust numerical method for a two dimensional reaction-diffusion problem
• The optimization of methods of solving boundary value problems with a boundary layer

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