Convergence analysis of the LDG method applied to singularly perturbed problems

DOI10.1002/num.21711zbMath1267.65157OpenAlexW2099888904MaRDI QIDQ4909183

Zhimin Zhang, Hui-Qing Zhu

Publication date: 12 March 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21711

zbMATH Keywords

numerical resultssingular perturbationuniform convergenceconvection-diffusion problemdiscontinuous Galerkin methoderror estimateShishkin meshexponential boundary layer

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (9)

Discontinuous Galerkin methods with interior penalties on graded meshes for 2D singularly perturbed convection-diffusion problems ⋮ Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem ⋮ Local discontinuous Galerkin method for a third-order singularly perturbed problem of convection-diffusion type ⋮ Local discontinuous Galerkin method for a third‐order singularly perturbed problem of reaction–diffusion type ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ Supercloseness result of higher order FEM/LDG coupled method for solving singularly perturbed problem on S-type mesh ⋮ A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems ⋮ Analysis of generalised alternating local discontinuous Galerkin method on layer-adapted mesh for singularly perturbed problems ⋮ Uniform convergence of the LDG method for a singularly perturbed problem with the exponential boundary layer

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