Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations

• Authors: Hailiang Liu;Michael Pollack
• Venue: Journal of Computational Physics
• Year: 2014

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.