A Central Discontinuous Galerkin Method for聽Hamilton-Jacobi Equations
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- 作者：Fengyan Li and Sergey Yakovlev
- 关键词：Discontinuous Galerkin method ; Central scheme ; Hamilton ; Jacobi equation ; Viscosity solution ; High order accuracy
- 刊名：Journal of Scientific Computing
- 出版时间：October 2010
- 出版年：2010
- 期刊代码：21_08857474
- 类别：edu
- 卷：45
- 期：1-3
- 页码：404-428
- 数据来源：sp
摘要
In this paper, a central discontinuous Galerkin method is proposed to solve for the viscosity solutions of Hamilton-Jacobi equations. Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation laws. They combine the central scheme and the discontinuous Galerkin method and therefore carry many features of both methods. Since Hamilton-Jacobi equations in general are not in the divergence form, it is not straightforward to design a discontinuous Galerkin method to directly solve such equations. By recognizing and following a “weighted-residual” or “stabilization-based” formulation of central discontinuous Galerkin methods when applied to hyperbolic conservation laws, we design a high order numerical method for Hamilton-Jacobi equations. The L 2 stability and the error estimate are established for the proposed method when the Hamiltonians are linear. The overall performance of the method in approximating the viscosity solutions of general Hamilton-Jacobi equations are demonstrated through extensive numerical experiments, which involve linear, nonlinear, smooth, nonsmooth, convex, or nonconvex Hamiltonians.