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://doi.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.