Error analysis of an extended discontinuous galerkin method for highly-oscillatory problems

French D., Vaughan B., Toprakseven Ş.

Sigma Journal of Engineering and Natural Sciences, cilt.39, ss.64-73, 2021 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39
  • Basım Tarihi: 2021
  • Doi Numarası: 10.14744/sigma.2021.00043
  • Dergi Adı: Sigma Journal of Engineering and Natural Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Sayfa Sayıları: ss.64-73
  • Anahtar Kelimeler: Discontinuous Galerkin, elliptic boundary value problem, extended discontinuous Galerkin, high frequencies
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

In this report we introduce an extended discontinuous Galerkin (XDG) method. Our XDG scheme is based on the Babuska-Zlamal approach and we apply it to a class of prototype elliptic boundary value problems that have solutions consisting of smooth functions perturbed by a set of high frequency modes which occupy a narrow band. The XDG scheme we study is enriched by trigonometric functions that cover the range of these perturbations. A theoretical error analysis is provided that shows the method converges and gives specifics on its accuracy. Computations with the XDG scheme further demonstrate the efficacy of this approach.