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	A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying time and space grids
	Tang, HZ ; Warnecke, G
	2005
关键词	Hamilton-Jacobi equation finite difference scheme local time step discretization Navier-Stokes equations DISCONTINUOUS GALERKIN METHOD CONSERVATION-LAWS VISCOSITY SOLUTIONS TRIANGULAR MESHES APPROXIMATIONS SYSTEMS
英文摘要	Based on a simple projection of the solution increments of the underlying partial differential equations (PDEs) at each local time level, this paper presents a difference scheme for nonlinear Hamilton-Jacobi (H-J) equations with varying time and space grids. The scheme is of good consistency and monotone under a local CFL-type condition. Moreover, one may deduce a conservative local time step scheme similar to Osher and Sanders scheme approximating hyperbolic conservation law (CL) from our scheme according to the close relation between CLs and H-J equations. Second order accurate schemes are constructed by combining the reconstruction technique with a second order accurate Runge-Kutta time discretization scheme or a Lax-Wendroff type method. They keep some good properties of the global time step schemes, including stability and convergence, and can be applied to solve numerically the initial-boundary-value problems of viscous H-J equations. They are also suitable to parallel computing. Numerical errors and the experimental rate of convergence in the L-p-norm, p = 1, 2, and ∞, are obtained for several one- and two-dimensional problems. The results show that the present schemes are of higher order accuracy.; Mathematics, Applied; SCI(E); EI; 12; ARTICLE; 4; 1415-1431; 26
语种	英语
出处	EI ; SCI
出版者	siam journal on scientific computing
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/315022]
专题	数学科学学院
推荐引用方式 GB/T 7714	Tang, HZ,Warnecke, G. A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying time and space grids. 2005-01-01.

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