Moving mesh discontinuous Galerkin methods for PDEs with traveling waves

Creative Commons License

UZUNCA M., KARASÖZEN B., Kucukseyhan T.

APPLIED MATHEMATICS AND COMPUTATION, cilt.292, ss.9-18, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 292
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.amc.2016.07.034
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9-18
  • Anahtar Kelimeler: Moving mesh, Discontinuous Galerkin, Nonlinear PDEs, Traveling wave, PARTIAL-DIFFERENTIAL-EQUATIONS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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. (C) 2016 Elsevier Inc. All rights reserved.