An $h$-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations

An $h$-Adaptive Runge-Kutta Discontinuous Galerkin Method for Hamilton-Jacobi Equations

Year:    2013

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 617–636

Abstract

In [35, 36], we presented an $h$-adaptive Runge-Kutta discontinuous Galerkin method using troubled-cell indicators for solving hyperbolic conservation laws. A tree data structure (binary tree in one dimension and quadtree in two dimensions) is used to aid storage and neighbor finding. Mesh adaptation is achieved by refining the troubled cells and coarsening the untroubled "children". Extensive numerical tests indicate that the proposed $h$-adaptive method is capable of saving the computational cost and enhancing the resolution near the discontinuities. In this paper, we apply this $h$-adaptive method to solve Hamilton-Jacobi equations, with an objective of enhancing the resolution near the discontinuities of the solution derivatives. One- and two-dimensional numerical examples are shown to illustrate the capability of the method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2013.1235nm

Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 617–636

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Runge-Kutta discontinuous Galerkin method h-adaptive method Hamilton-Jacobi equation.

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