A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions
Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 154–177
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-563
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 1 : pp. 154–177
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Hamilton-Jacobi equations discontinuous Galerkin method local discontinuous Galerkin method a priori error estimates.