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$L^\infty$ estimation of the LDG method for 1-d singularly perturbed convection-diffusion problems

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  • Pointwise error estimates of the local discontinuous Galerkin (LDG) method for a one-dimensional singularly perturbed problem are studied. Several uniform $L^\infty$ error bounds for the LDG approximation to the solution and its derivative are established on a Shishkin-type mesh. Numerical experiments are presented.
    Mathematics Subject Classification: Primary: 65L10, 65L11; Secondary: 65L60, 65L20.

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    H. Zhu and Z. ZhangPointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems, Comput. Methods Appl. Math., Published Online: 10/19/2012. doi: 10.1515/cmam--2012--0004.

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