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首页> 外文期刊>Journal of Scientific Computing >Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations
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Local-Structure-Preserving Discontinuous Galerkin Methods with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi Equations

机译：Hamilton-Jacobi方程的Lax-Wendroff型时间离散化的保留局部结构的不连续Galerkin方法

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摘要

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.
机译：本文设计了一系列高阶数值方法来求解Hamilton-Jacobi方程的粘度解。特别是，这些方法从与汉密尔顿-雅各比方程密切相关的双曲守恒定律系统开始。然后将紧凑的一步式一级Lax-Wendroff型时间离散化与保留局部结构的不连续Galerkin空间离散化一起应用。与某些标准数值方法相比，所得方法在结构化和非结构化网格上均具有较低的计算复杂度和内存使用量，同时它们能够准确可靠地捕获Hamilton-Jacobi方程的粘度解。提出了一组数值实验，以说明该方法的性能。

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