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Moving mesh discontinuous Galerkin methods for PDEs with traveling waves

Author

Listed:
  • Uzunca, M.
  • Karasözen, B.
  • Küçükseyhan, T.

Abstract

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 Schlögl (Nagumo) equations.

Suggested Citation

  • Uzunca, M. & Karasözen, B. & Küçükseyhan, T., 2017. "Moving mesh discontinuous Galerkin methods for PDEs with traveling waves," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 9-18.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:9-18
    DOI: 10.1016/j.amc.2016.07.034
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    References listed on IDEAS

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    1. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 153-185, September.
    2. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "Erratum to: On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 187-188, September.
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    Cited by:

    1. Castillo, Paul & Gómez, Sergio & Manzanarez, Sergio, 2019. "Improving the accuracy of LDG approximations on coarse meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 310-326.

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