Moving mesh discontinuous Galerkin methods for PDEs with traveling waves

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2017-01-01

Author

UZUNCA, MURAT
Karasözen, Bülent
Kucukseyhan, T.

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In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the efficiency of the proposed moving mesh dG method for solving Burgers', Burgers'-Fisher and Schlogl (Nagumo) equations.

Subject Keywords

Moving mesh, Discontinuous Galerkin, Nonlinear PDEs, Traveling wave

URI

https://hdl.handle.net/11511/32212

Journal

APPLIED MATHEMATICS AND COMPUTATION

DOI

https://doi.org/10.1016/j.amc.2016.07.034

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. UZUNCA, B. Karasözen, and T. Kucukseyhan, “Moving mesh discontinuous Galerkin methods for PDEs with traveling waves,” APPLIED MATHEMATICS AND COMPUTATION, pp. 9–18, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32212.