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Local Analysis of the Local Discontinuous Galerkin Method with Generalized Alternating Numerical Flux for One-Dimensional Singularly Perturbed Problem

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Abstract

In this paper we would like to present the local analysis of the local discontinuous Galerkin method based on the generalized alternating numerical flux for the one-dimensional time-dependent singularly perturbed problem with a stationary boundary layer. By virtue of the generalized Gauss–Radau projection and energy technique with suitable weight function, we can obtain the double-optimal local error estimate that the convergence rate in \(\hbox {L}^2\)-norm out of the pollution region nearby the outflow boundary is optimal, and the width of pollution region is quasi-optimal also. Numerical experiments are given.

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Authors and Affiliations

  1. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, Jiangsu Province, People’s Republic of China

    Yao Cheng

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu Province, People’s Republic of China

    Qiang Zhang

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  1. Yao Cheng
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  2. Qiang Zhang
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Correspondence to Qiang Zhang.

Additional information

Yao Cheng: Research supported by NSFC Grant 11271187.

Qiang Zhang: Research supported by NSFC Grants 11271187, 11571290 and 11671199.

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Cheng, Y., Zhang, Q. Local Analysis of the Local Discontinuous Galerkin Method with Generalized Alternating Numerical Flux for One-Dimensional Singularly Perturbed Problem. J Sci Comput 72, 792–819 (2017). https://doi.org/10.1007/s10915-017-0378-y

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  • DOI: https://doi.org/10.1007/s10915-017-0378-y

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