Name
Abstract | ||
|---|---|---|
In this paper we propose a new local discontinuous Galerkin method to directly solve Hamilton-Jacobi equations. The scheme is a natural extension of the monotone scheme. For the linear case with constant coefficients, the method is equivalent to the discontinuous Galerkin method for conservation laws. Thus, stability and error analysis are obtained under the framework of conservation laws. For both convex and noneconvex Hamiltonian, optimal (k+1)th order of accuracy for smooth solutions are obtained with piecewise kth order polynomial approximations. The scheme is numerically tested on a variety of one and two dimensional problems. The method works well to capture sharp corners (discontinuous derivatives) and have the solution converges to the viscosity solution. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcp.2010.09.022 | J. Comput. Physics |
Keywords | Field | DocType |
discontinuous derivative,piecewise kth order polynomial,discontinuous galerkin method,monotone scheme,hamilton-jacobi equation,smooth solution,new local discontinuous galerkin,conservation law,viscosity solution,local discontinuous galerkin method,solution converges,th order | Discontinuous Galerkin method,Order of accuracy,Mathematical optimization,Mathematical analysis,Hamilton–Jacobi equation,Constant coefficients,Viscosity solution,Conservation law,Discontinuous Deformation Analysis,Mathematics,Piecewise | Journal |
Volume | Issue | ISSN |
230 | 1 | Journal of Computational Physics |
Citations | PageRank | References |
21 | 1.08 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jue Yan | 1 | 198 | 24.23 |
| Stanley Osher | 2 | 7973 | 514.62 |