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

Huiqing Zhu; Runchang Lin

doi:10.3934/dcdsb.2013.18.1493

Article Contents

2013, Volume 18, Issue 5: 1493-1505. Doi: 10.3934/dcdsb.2013.18.1493

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

Huiqing Zhu^1, and
Runchang Lin^2,

1.
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406
2.
Department of Engineering, Mathematics, and Physics, Texas A&M International University, Laredo, TX 78041

Received: April 2012

Revised: October 2012

Published: July 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 65L10, 65L11; Secondary: 65L60, 65L20.

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