TY - JOUR T1 - A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 154 EP - 177 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/563.html KW - Hamilton-Jacobi equations, discontinuous Galerkin method, local discontinuous Galerkin method, a priori error estimates. AB -

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.