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

Akman T.

APPLICABLE ANALYSIS, vol.96, no.3, pp.461-482, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1080/00036811.2016.1143930
  • Journal Name: APPLICABLE ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.461-482
  • Middle East Technical University Affiliated: Yes

Abstract

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.