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Volume 35, Issue 3
Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem

Yao Cheng & Qiang Zhang

DOI: 10.4208/jcm.1605-m2015-0398

J. Comp. Math., 35 (2017), pp. 265-288.

Published online: 2017-06

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  • Abstract

In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.

  • Keywords

Local analysis, Runge-Kutta method, Local discontinuous Galerkin method, Singularly perturbed problem, Boundary layer.

  • AMS Subject Headings

65M15, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ycheng@smail.nju.edu.cn (Yao Cheng)

qzh@nju.edu.cn (Qiang Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-265, author = {Cheng , Yao and Zhang , Qiang}, title = {Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {3}, pages = {265--288}, abstract = {

In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2015-0398}, url = {http://global-sci.org/intro/article_detail/jcm/9773.html} }
TY - JOUR T1 - Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem AU - Cheng , Yao AU - Zhang , Qiang JO - Journal of Computational Mathematics VL - 3 SP - 265 EP - 288 PY - 2017 DA - 2017/06 SN - 35 DO - http://doi.org/10.4208/jcm.1605-m2015-0398 UR - https://global-sci.org/intro/article_detail/jcm/9773.html KW - Local analysis, Runge-Kutta method, Local discontinuous Galerkin method, Singularly perturbed problem, Boundary layer. AB -

In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.

Cheng , Yao and Zhang , Qiang. (2017). Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem. Journal of Computational Mathematics. 35 (3). 265-288. doi:10.4208/jcm.1605-m2015-0398
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