A Priori Error Estimates for Semi-Discrete Discontinuous Galerkin Methods Solving Nonlinear Hamilton-Jacobi Equations with Smooth Solutions

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.