TY - JOUR
T1 - The Relaxing Schemes for Hamilton-Jacobi Equations
AU - Tang , Hua-Zhong
AU - Wu , Hua-Mu
JO - Journal of Computational Mathematics
VL - 3
SP - 231
EP - 240
PY - 2001
DA - 2001/06
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8976.html
KW - The relaxing scheme, The relaxing systems, Hamilton-Jacobi equation, Hyperbolic conservation law.
AB - <p style="text-align: justify;">Hamilton-Jacobi equation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for Hamilton-Jacobi equations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.</p>