The \(hp\)- and \(h\)-versions of the discontinuous and local discontinuous Galerkin methods for one-dimensional singularly perturbed models

DOI10.1016/J.APNUM.2011.08.001zbMath1242.65147OpenAlexW1985960276MaRDI QIDQ651083

Kassem Mustapha

Publication date: 8 December 2011

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.08.001

zbMATH Keywords

convection-diffusion problemboundary layersShishkin meshexponential convergencealgebraic convergencelocal discontinuous Galerkin method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) 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 (2)

Nodal superconvergence of the local discontinuous Galerkin method for singularly perturbed problems ⋮ Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods

Cites Work

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• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
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• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• The $p$ and $hp$ versions of the finite element method for problems with boundary layers
• Galerkin Finite Element Methods for Parabolic Problems

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