A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 21 (2) , 666-690
- https://doi.org/10.1137/s1064827598337282
Abstract
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton--Jacobi equations. This method is based on the Runge--Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high-order accuracy with a local, compact stencil, and is suited for efficient parallel implementation. One- and two-dimensional numerical examples are given to illustrate the capability of the method. At least kth order of accuracy is observed for smooth problems when kth degree polynomials are used, and derivative singularities are resolved well without oscillations, even without limiters.This publication has 22 references indexed in Scilit:
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