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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

    Wei Guo & Jianxian Qiu

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Fengyan Li

  3. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, P.R. China

    Jianxian Qiu

Authors
  1. Wei Guo
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  2. Fengyan Li
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  3. Jianxian Qiu
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Corresponding author

Correspondence to Jianxian Qiu.

Additional information

F. Li was supported in part by the NSF grant DMS-0652481, NSF CAREER award DMS-0847241 and an Alfred P. Sloan Research Fellowship.

J. Qiu was supported in part by NSFC grants 10931004, 1081112028 and 10871093.

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Guo, W., Li, F. & Qiu, J. Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations. J Sci Comput 47, 239–257 (2011). https://doi.org/10.1007/s10915-010-9434-6

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  • DOI: https://doi.org/10.1007/s10915-010-9434-6

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