TY - JOUR
T1 - A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions
AU - Tao Xiong, Chi-Wang Shu & Mengping Zhang
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 - <p style="text-align: justify;">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.</p>