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Volume 10, Issue 1
A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions

Tao Xiong, Chi-Wang Shu & Mengping Zhang

Int. J. Numer. Anal. Mod., 10 (2013), pp. 154-177.

Published online: 2013-10

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  • 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.

  • Keywords

Hamilton-Jacobi equations, discontinuous Galerkin method, local discontinuous Galerkin method, a priori error estimates.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-10-154, author = {Tao Xiong, Chi-Wang Shu and Mengping Zhang}, title = {A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/563.html} }
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 -

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.

Tao Xiong, Chi-Wang Shu and Mengping Zhang. (2013). A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions. International Journal of Numerical Analysis and Modeling. 10 (1). 154-177. doi:
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