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 differenc...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 HamiltonJacobi 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.展开更多
Presents a study which examined a cell entropy inequality for a class of local relaxation approximation relaxing scheme for scalar conservation laws. Way to obtain the scheme; Use of numerical entropy condition for th...Presents a study which examined a cell entropy inequality for a class of local relaxation approximation relaxing scheme for scalar conservation laws. Way to obtain the scheme; Use of numerical entropy condition for the approximation.展开更多
Presents a study on the cell entropy inequality for two classes of fully discrete relaxing schemes approximating scalar conservation laws. Main advantage of the schemes; Review of the construction of the relaxing syst...Presents a study on the cell entropy inequality for two classes of fully discrete relaxing schemes approximating scalar conservation laws. Main advantage of the schemes; Review of the construction of the relaxing system with a stiff source term; Conclusions.展开更多
基金the National Natural Science Foundation of China (Grant No. 19901031)and the foundation of National Laboratory of Computationa
文摘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 HamiltonJacobi 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.
文摘Presents a study which examined a cell entropy inequality for a class of local relaxation approximation relaxing scheme for scalar conservation laws. Way to obtain the scheme; Use of numerical entropy condition for the approximation.
基金National Natural Science Foundation (No.19901031), Special Funds for Major State Basic Research Projects of China, and the Found
文摘Presents a study on the cell entropy inequality for two classes of fully discrete relaxing schemes approximating scalar conservation laws. Main advantage of the schemes; Review of the construction of the relaxing system with a stiff source term; Conclusions.
基金National Natural Science Foundation of ChinaLaboratory of Computational Physics of Beijing IAPCM
文摘Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.
