Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations

Authors:
Wei Guo;Fengyan Li;Jianxian Qiu
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, USA 12180;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093 and School of Mathematical Sciences, Xiamen University, Xiamen, P.R. China 361005
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

In this paper, a family of high order numerical methods are designed to solve the Hamilton-Jacobi equation for the viscosity solution. In particular, the methods start with a hyperbolic conservation law system closely related to the Hamilton-Jacobi equation. The compact one-step one-stage Lax-Wendroff type time discretization is then applied together with the local-structure-preserving discontinuous Galerkin spatial discretization. The resulting methods have lower computational complexity and memory usage on both structured and unstructured meshes compared with some standard numerical methods, while they are capable of capturing the viscosity solutions of Hamilton-Jacobi equations accurately and reliably. A collection of numerical experiments is presented to illustrate the performance of the methods.