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Volume 14, Issue 4-5
A Priori Error Analysis of the Local Discontinuous Galerkin Method for the Viscous Burgers-Poisson System

Nattapol Ploymaklam, Pratik M. Kumbhar & Amiya K. Pani

Int. J. Numer. Anal. Mod., 14 (2017), pp. 784-807.

Published online: 2017-08

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  • Abstract

In this paper, we propose and analyze the local discontinuous Galerkin method for the viscous Burgers-Poisson system. The proposed method preserves two invariants and hence, yields solutions even for long time. A priori error estimates, which are of order $\mathcal{O}(h^{k+1})$, when polynomials of degree $k\geq 1$ are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.

  • Keywords

Burgers-Poisson system, local discontinuous Galerkin method, A priori error estimates.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-784, author = {Nattapol Ploymaklam, Pratik M. Kumbhar and Amiya K. Pani}, title = {A Priori Error Analysis of the Local Discontinuous Galerkin Method for the Viscous Burgers-Poisson System}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {784--807}, abstract = {

In this paper, we propose and analyze the local discontinuous Galerkin method for the viscous Burgers-Poisson system. The proposed method preserves two invariants and hence, yields solutions even for long time. A priori error estimates, which are of order $\mathcal{O}(h^{k+1})$, when polynomials of degree $k\geq 1$ are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10061.html} }
TY - JOUR T1 - A Priori Error Analysis of the Local Discontinuous Galerkin Method for the Viscous Burgers-Poisson System AU - Nattapol Ploymaklam, Pratik M. Kumbhar & Amiya K. Pani JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 784 EP - 807 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10061.html KW - Burgers-Poisson system, local discontinuous Galerkin method, A priori error estimates. AB -

In this paper, we propose and analyze the local discontinuous Galerkin method for the viscous Burgers-Poisson system. The proposed method preserves two invariants and hence, yields solutions even for long time. A priori error estimates, which are of order $\mathcal{O}(h^{k+1})$, when polynomials of degree $k\geq 1$ are used for approximating solutions are established. Finally, numerical experiments are conducted to confirm our theoretical results.

Nattapol Ploymaklam, Pratik M. Kumbhar and Amiya K. Pani. (2017). A Priori Error Analysis of the Local Discontinuous Galerkin Method for the Viscous Burgers-Poisson System. International Journal of Numerical Analysis and Modeling. 14 (4-5). 784-807. doi:
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