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

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

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.

• Content Type Journal Article
• DOI 10.1007/s10915-010-9434-6
• Authors
  
  
  • Wei Guo, Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, P.R. China
  • Fengyan Li, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
  • Jianxian Qiu, Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, P.R. China
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

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