A priori error estimates for semi-discrete discontinuous Galerkin methods solving nonlinear Hamilton-Jacobi equations with smooth solutions

摘要

In this paper, we provide a priori L~2 error estimates for the semi-discrete discontinuous Galerkin method [3] and the local discontinuous Galerkin method [22] for one- and two-dimensional nonlinear Hamilton-Jacobi equations with smooth solutions. With a special Gauss-Radau projection, the optimal error estimates on rectangular meshes are obtained.