The Effect of the Least Square Procedure for Discontinuous Galerkin Methods for Hamilton-Jacobi Equations

Abstract

In this presentation, we perform further investigation on the least square procedure used in the discontinuous Galerkin methods developed in [2] and [3] for the two-dimensional Hamilton-Jacobi equations. The focus of this presentation will be upon the influence of this least square procedure to the accuracy and stability of the numerical results. We will show through numerical examples that the procedure is crucial for the success of the discontinuous Galerkin methods developed in [2] and [3], especially for high order methods. New test cases using P ⁴ polynomials, which are at least fourth order and often fifth order accurate, are shown, in addition to the P ² and P ³ cases presented in [2] and [3]. This addition is non-trivial as the least square procedure plays a more significant role for the P ⁴ case.