Name
Abstract | ||
|---|---|---|
In this work, we propose a high resolution Alternating Evolution Discontinuous Galerkin (AEDG) method to solve Hamilton-Jacobi equations. The construction of the AEDG method is based on an alternating evolution system of the Hamilton-Jacobi equation, following the previous work Liu et al. (2013) [31] on AE schemes for Hamilton-Jacobi equations. A semi-discrete AEDG scheme derives directly from a sampling of this system on alternating grids. Higher order accuracy is achieved by a combination of high-order polynomial approximation near each grid and a time discretization with matching accuracy. The AEDG methods have the advantage of easy formulation and implementation, and efficient computation of the solution. For the linear equation, we prove the L^2 stability of the method. Numerical experiments for a set of Hamilton-Jacobi equations are presented to demonstrate both accuracy and capacity of these AEDG schemes. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcp.2013.09.038 | J. Comput. Physics |
Keywords | Field | DocType |
galerkin method,evolution system,hamilton-jacobi equation,alternating evolution,linear equation,ae scheme,aedg scheme,previous work,aedg method,semi-discrete aedg scheme,higher order accuracy,evolution discontinuous galerkin,viscosity solution | Discontinuous Galerkin method,Discretization,Linear equation,Mathematical optimization,Polynomial,Mathematical analysis,Sampling (statistics),Viscosity solution,Mathematics,Grid,Computation | Journal |
Volume | ISSN | Citations |
258, | 0021-9991 | 2 |
PageRank | References | Authors |
0.40 | 12 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hailiang Liu | 1 | 39 | 6.57 |
| Michael Pollack | 2 | 7 | 1.22 |