The accuracy of an HDG method for conservative fractional diffusion equations


Karaaslan M. F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.41, pp.8201-8211, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41
  • Publication Date: 2018
  • Doi Number: 10.1002/mma.5282
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.8201-8211
  • Yıldız Technical University Affiliated: Yes

Abstract

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.