Volume 16, Issue 2
Spectral Element Viscosity Methods for Nonlinear Conservaion Laws on the Semi-Infinte Interval

L. Jiang & C. J. Xu

DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 112-130

Published online: 2007-05

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  • Abstract

In this paper we propose a spectral element vanishing viscosity (SEVV) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this transformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEVV approximation converges to the unique entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results.

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@Article{NM-16-112, author = { L. Jiang and C. J. Xu }, title = {Spectral Element Viscosity Methods for Nonlinear Conservaion Laws on the Semi-Infinte Interval}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {2}, pages = {112--130}, abstract = { In this paper we propose a spectral element vanishing viscosity (SEVV) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this transformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEVV approximation converges to the unique entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8050.html} }
TY - JOUR T1 - Spectral Element Viscosity Methods for Nonlinear Conservaion Laws on the Semi-Infinte Interval AU - L. Jiang & C. J. Xu JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 112 EP - 130 PY - 2007 DA - 2007/05 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/nm/8050.html KW - AB - In this paper we propose a spectral element vanishing viscosity (SEVV) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this transformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEVV approximation converges to the unique entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results.
L. Jiang & C. J. Xu . (1970). Spectral Element Viscosity Methods for Nonlinear Conservaion Laws on the Semi-Infinte Interval. Numerical Mathematics, a Journal of Chinese Universities. 16 (2). 112-130. doi:
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