@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} }