The accuracy of an HDG method for conservative fractional diffusion equations

KARAASLAN M. F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.41, sa.17, ss.8201-8211, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 17
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/mma.5282
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.8201-8211
  • Anahtar Kelimeler: Caputo derivative, conservative-fractional diffusion equation, hybridization, hybridizable discontinuous Galerkin methods, FINITE-ELEMENT-METHOD, DISPERSION
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this paper, we introduce and investigate the performance of a hybridizable discontinuous Galerkin (HDG) method for approximating the solution of conservative fractional diffusion equations (CFDE). The main attractive feature of these methods is the fact that the only globally coupled unknowns are those at the element boundaries. We first introduce the HDG method for the CFDE and prove the existence and uniqueness of the numerical solution provided that the stabilization parameter is strictly positive. We provide extensive numerical results to test the convergence behavior of the HDG approximation.