Error estimates for space-time discontinuous Galerkin formulation based on proper orthogonal decomposition

Akman T.

APPLICABLE ANALYSIS, cilt.96, sa.3, ss.461-482, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 96 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/00036811.2016.1143930
  • Dergi Adı: APPLICABLE ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.461-482
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this study, proper orthogonal decomposition (POD) method is applied to diffusion-convection-reaction equation, which is discretized using spacetime discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and spacetime projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.