TY - JOUR
T1 - A New Class of Uniformly Second Order Accurate Difference Schemes for 2D Scalar Conservation Laws
AU - Cheng , Juan
AU - Dai , Jiazun
JO - Journal of Computational Mathematics
VL - 4
SP - 311
EP - 318
PY - 1997
DA - 1997/08
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9208.html
KW - 
AB - <p style="text-align: justify;">In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws, we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the convergence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak $L^{\infty}$-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.</p>