Paper Info
Title
A new discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations.
Abstract
In this paper, we improve upon the discontinuous Galerkin (DG) method for Hamilton–Jacobi (HJ) equation with convex Hamiltonians in [5] and develop a new DG method for directly solving the general HJ equations. The new method avoids the reconstruction of the solution across elements by utilizing the Roe speed at the cell interface. Besides, we propose an entropy fix by adding penalty terms proportional to the jump of the normal derivative of the numerical solution. The particular form of the entropy fix was inspired by Harten and Hyman's entropy fix [12] for Roe scheme for the conservation laws. The resulting scheme is compact, simple to implement even on unstructured meshes, and is demonstrated to work for nonconvex Hamiltonians. Benchmark numerical experiments in one dimension and two dimensions are provided to validate the performance of the method.
Year
DOI
Venue
2014
10.1016/j.jcp.2014.02.041
Journal of Computational Physics
Keywords
DocType
Volume
Hamilton–Jacobi equation,Discontinuous Galerkin methods,Entropy fix,Unstructured mesh
Journal
268
ISSN
Citations 
PageRank 
0021-9991
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Yingda Cheng120120.27
Zixuan Wang2205.18